The expression [tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx[/tex] is an illustration of definite integrals
The approximated value of the definite integral is 0.0059
How to evaluate the definite integral?The definite integral is given as:
[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx[/tex]
For arctan(x), we have the following series equation:
[tex]\arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1}}{2n + 1}}[/tex]
Multiply both sides of the equation by x^3.
So, we have:
[tex]x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1}}{2n + 1}} * x^3[/tex]
Apply the law of indices
[tex]x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1 + 3}}{2n + 1}}[/tex]
[tex]x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}[/tex]
Evaluate the product
[tex]x^3 \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}[/tex]
Introduce the integral sign to the equation
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =\int\limits^{1/2}_{0} \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}[/tex]
Integrate the right hand side
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}} ]\limits^{1/2}_{0}[/tex]
Expand the equation by substituting 1/2 and 0 for x
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}} ] - [ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{0^{2n + 4}}{2n + 1}} ][/tex]
Evaluate the power
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}} ] - 0[/tex]
[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}}[/tex]
The nth term of the series is then represented as:
[tex]T_n = \frac{(-1)^n}{2^{2n + 5} * (2n + 4)(2n + 1)}[/tex]
Solve the series by setting n = 0, 1, 2, 3 ..........
[tex]T_0 = \frac{(-1)^0}{2^{2(0) + 5} * (2(0) + 4)(2(0) + 1)} = \frac{1}{2^5 * 4 * 1} = 0.00625[/tex]
[tex]T_1 = \frac{(-1)^1}{2^{2(1) + 5} * (2(1) + 4)(2(1) + 1)} = \frac{-1}{2^7 * 6 * 3} = -0.0003720238[/tex]
[tex]T_2 = \frac{(-1)^2}{2^{2(2) + 5} * (2(2) + 4)(2(2) + 1)} = \frac{1}{2^9 * 8 * 5} = 0.00004340277[/tex]
[tex]T_3 = \frac{(-1)^3}{2^{2(3) + 5} * (2(3) + 4)(2(3) + 1)} = \frac{-1}{2^{11} * 10 * 7} = -0.00000634131[/tex]
..............
At n = 2, we can see that the value of the series has 4 zeros before the first non-zero digit
This means that we add the terms before n = 2
This means that the value of [tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx[/tex] to 4 decimal points is
[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.00625 - 0.0003720238[/tex]
Evaluate the difference
[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.0058779762[/tex]
Approximate to four decimal places
[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.0059[/tex]
Hence, the approximated value of the definite integral is 0.0059
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A computer’s memory is composed of 8k words of 32 bits each. how many total bytes in memory?
The number of total bytes in memory is 32,000 bytes.
How many total bytes in memory?
We know that the memory is composed of 8k (or 8,000) words of 32 bits each.
To get the total memory, we just need to take the product between the number of words and the memory that each has.
This will give:
8,000*(32 bits) = 256,000 bits.
But we want this in bytes so we need to change the units, remember that:
1 bit = 0.125 byte.
Then we have:
256,000 bits = 256,000*( 0.125 byte) = 32,000 bytes.
The memory has 32,000 bytes in total.
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The character of su-jen is mainly revealed through her —
There are different kinds of character. The character of Su-Jen is mainly revealed through her thoughts.
What was the except about?The story about Su-Jen is gotten from a novel that was written about Su-Jen, a young girl who had to go all the way to China from US. along with her to meet her father.
It was a first time meeting for Su-Jen and it was an emotional one. All the character seen about Su-Jen is from her thoughts that were written out.
See options below
actions
dialogue
appearance
thoughts
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When a strontium atom loses two electrons to form an sr2+ ion, the electrons are lost from the
Answer:
5s orbital
Explanation:
Answer:
Answer: When a strontium atom loses two electrons, it becomes a(n) cation with a charge of 2+. when any neutral atom loses an electron it becomes a cation that is positively charged ions and an ion gets the charge according to the number of electrons loses. 5s orbital
Explanation:
Linear algebra with applications 8th edition solutions
Answer:
That makes 21
Whats your question?
What do you need help on?
I took algebra a while ago so I may be able to help you.
Explanation:
Module 11 angle relationships in parallel lines and triangles answer key
An example of Module 11 angle relationships in parallel lines and triangles question is give in the image attached. The answer (Image attached) to the question is ∠8 and ∠1 .
What are the examples of Angles of Parallel Lines?Angles can be said to be directly opposite each other and they are known as vertical angles which are said to be congruent.
Alternate interior angles and alternate exterior angles are known to be two other pairs of corresponding angles that are also said to be congruent.
The angle ∠8 and ∠1 are pair of angles are alternate exterior angles because they are pair of angles on the outer side of a specific two parallel lines but are found to be on the opposite side of the transversal as shown in the image.
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Subshells half-filled with electrons are particularly stable. can you suggest a possible physical basis for this claim?
The physical basis for this claim is that all orbitals need to have like one electron at least to hinder repulsion by the action of pairing of element.
What the ways that electrons are filled in Subshells?Shells and subshells are known to be filled in the level of energy order, and as such, electrons need to fill the 4s subshell before they can be able to fill 3d shell.
Note that Orbitals are often and singly filled by electrons and can double up only when all orbitals has like one electron to hinder repulsion by the action of pairing of element.
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in part two of trifles, which of the following most supports the feminist theme that women suffer abuses within a male-dominated society?
The statement that mosupports the feminist theme that women suffer abuses within a male-dominated society is: the bird with the broken neck.
TriflesThe bird with the broken neck best support the feminist theme as it best depict the different abuses women pass through.
It showcase or represent what women endure in their marriages as well as how women are maltreated in a society that in male dominated.
Therefore the statement that supports the feminist theme is: the bird with the broken neck.
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the office of constable has changed significantly in some parts of texas. critics of constables often make which two of the following points when talking about the expansion of their roles?
The points when talking about the expansion of their roles are:
Constables do face some small oversight from other officials.Constable offices can be said to be a half-militarized fiefdoms.Who is a Constable?A constable is known to be an individual that is said to be in specific office or position, mostly in terms of carrying out criminal law.
Note that the office of constable do differs a lot significantly and also differs in the area of jurisdictions. A constable is said to be rank, an officer that is found within the police force.
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What obstacle was faced by the union pacific railroad workers but not the central pacific workers? steep mountains conflict with american indians harsh weather conditions worker shortages
An obstacle which was faced by the union pacific railroad workers but not the central pacific workers is: B. conflict with American Indians.
Who are union pacific railroad workers?The union pacific railroad workers can be defined as a group of young Civil War veterans and Irish immigrants that were saddled with the responsibility of providing railroad related services to commuters.
Unlike the central pacific workers, an obstacle which was directly faced and experienced by the union pacific railroad workers is conflict with American Indians (Native Americans) because the American Indians wanted to reclaim the jobs and way of life that was being taken away from them.
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I know I am a week late but for the future people the answer is A,C,D,F.
I got it right on edge.
The other aswer to the second question is B.
Got it right on edge, Have a good day <3.
Let w be the union of the first and third quadrants
Answer:
union mean between so the. first n second quadrants are at 180 degree so we will divide my 2 n then get the answer to be 90
A student knows the mass of one of the reactants of a chemical reaction and wants to calculate the mass of one of the products of the reaction. which process should the student follow?
There are different ways to calculate math. What the student is to do in the above scenario are:
To Multiply the mass of the reactant by its molar mass to find the number of moles of the reactant. Use the chemical equation to find the number of moles of the product. Divide the number of moles of the product by its molar mass to find the mass of the product.
What is the mass of reactant?The law of conservation of mass is one that states that in form of chemical reaction, the total mass of reactants is known and regarded as equal to the total mass of products.
The steps in mass calculations are mass = moles × molar mass
Calculate moles = mass(Mg) ÷ molar mass, moles.
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Identify the median for the given data? 23, 34, 27, 7, 30, 26, 28, 31, 34
Explanation:
Arrange from ascending to descending order
7,23,26,27] ,28, [30,31,34,34
median is 28
which of the following is one of the reasons to debrief after doing an event when using the abcd model?
A reasons to debrief after doing an event while using the ABCD model is to make the communication of issues simple and plain.
What is an ABCD model?An ABCD model is an abbreviation for assumption based communication dynamics model and it can be defined as a strategic methodology that allows a project manager or business organization to capture differing opinions, viewpoints and knowledge from respective stakeholders, so as to enhance the swift communication of issues and ensures a proactive management of associated risks.
Based on the assumption based communication dynamics (ABCD) model, it is important to debrief after doing an event because it provides a simple language for the communication of risk to various departments of a business organization.
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A real estate agent working in a large city believes that
A real estate agent working in a large city believes for three-bedroom houses, the selling price decreases by $2,000 for every mile increase in the distance of the house from the city center.
Who is an Agent?This is an individual who is empowered to act on behalf of another and is used in various sectors such as sports, housing etc.
From the graph, we can infer that the selling price decreases by approximately $2,000 for every mile increase in the distance of the house from the city center.
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Which type of growth is best illustrated by this rabbit population?
The type of growth that is best illustrated by the rabbit population is; exponential growth.
What is the population growth?Looking the graph giving illustrated by the rabbit population seen online, it is clear that the number of individual in that population continually increase until a maximum point was reached. Thereafter, there was a slight decline in the population.
Finally, the maximum point reached on the graph is the carrying point and the value from the graph is about 0.4 million and we can say that this depicts an exponential growth model.
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David poole linear algebra 4th edition solutions pdf
There are a lot of math problem. An example of David Poole linear algebra 4th edition work is linear equation.
What is the linear algebra 4th edition about?Linear Algebra is known to be a type of a modern breakthrough or an introduction that was made by David Poole Trent University. It handles a lot of issues regarding algebra.
An example of linear equation is The value of c for that has the pair of equations: cx – y = 2 and 6x – 2y = 3 is what?. The answer too the above is 3.
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What phrase is repeated in this passage? what idea is emphasized through repetition?
Answer:
Q: What phrase is repeated in this passage?
A: Go Back
Q: What idea is emphasized through repetition?
A: Returning home with renewed hope
Explanation:
Got it right on edge!
What phrase is repeated in this passage A: Go Back. What idea is emphasized through repetition? Returning home with renewed hope.
What is Repetition?Repetition is the straightforward repetition of a word within a condensed number of words (including in a poem), without specific word placement to ensure emphasis.
It is a multilingual written or spoken device that is often employed in Hindi and Mandarin in addition to English. As a result, it is rarely referred to as a figure of speech.
Its forms, many of which are described below, have various resonances to listing (forms of enumeration, such as "First, Second, Third, and Last..."), and, as a matter of trite logic, frequently have effects that are comparable to each other.
Therefore, What phrase is repeated in this passage A: Go Back. What idea is emphasized through repetition? Returning home with renewed hope.
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#SPJ7
The parents of a little girl who keeps a mare in their backyard agree to take the mare down the road to be serviced by a stallion at a breeding facility. sometime after the mare returns, she develops a thick mucus discharge from her nose and has a swelling under her jaw. this mare should have been vaccinated against
a) strangles.
b) botulism.
c) rabies.
d) potomac horse fever.
Use rules of inference to show that the hypothesis
ratio + L + no one asked + bozo +
Mike is hanging a string of lights on his barn for a square dance
Chavez is studying the relationship between emotions and physiological reactions. he believes that the different emotions experienced by individuals cannot be associated with specific physiological changes because autonomic nervous system responses are too diffuse and slow to account for rapid and differentiated emotional responses. in this context, chavez is most likely to reject
Chávez's claim that the autonomic nervous system is too diffuse and slow to explain rapid and differentiated emotional responses is wrong.
The autonomic nervousThis system regulates certain body processes such as blood pressure and respiratory rate. It works automatically (autonomously) without the person's conscious effort.
The path of an autonomic nerve involves two nerve cells. One of them is located in the brain stem or spinal cord. It is connected by nerve fibers to another cell, located in a group of nerve cells (called autonomic ganglia). Nerve fibers from these ganglia connect with internal organs.
With these information, we can conclude that Chávez's claim that the autonomic nervous system is too diffuse and slow to explain rapid and differentiated emotional responses is wrong.
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What is the probability that a player will toss the die at least 2 times before blue lands faceup?
The probability that a player will toss the die at least 2 times before blue lands faceup is 0.5625.
What is Probability?This is known to be an aspect of mathematics that deals with numerical depiction of how likely an item is to take place or occur or not.
Note that in the scenario above, for each toss, there are only two possible outcomes, either blue lands face up, or not and as such
2 outcome out of the 8 faces which are blue is =
p = 2/8 = 0.25
P (X = 0) = C₂.₀(0.25)⁰. (0.75)₂ = 0.5625
Therefore, the answer is 0.5625
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Decide if the following sentence is grammatically correct or incorrect. tú diríamos la historia. correct incorrect
Answer:
Incorrect
Explanation:
Answer:
incorrect
Explanation:
edge 2021
which diagram best represents the efficient extraction of oxygen from water by the mechanism of countercurrent exchange?
The diagram that best represents the efficient extraction of oxygen is the diagram, where oxygen gradient do exists with the full length of the capillary.
What is the extraction of oxygen?The term Oxygen extraction fraction (OEF) is known to be a term that connote the rate of blood oxygen that a tissue often absorbed from the blood flow to keep function and morphological state.
Note that the OEF shows the efficiency of oxygen use by the tissue and, so it is a hemodynamic way of measurement in brain ischemia.
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Find the dimensions of a rectangle (in m) with perimeter 68 m whose area is as large as possible. (enter the dimensions as a comma-separated list.)
The dmension of the rectangle with perimeter of 68 m has the largest possible area as 17m by 17m.
Perimeter of a rectangleperimeter of rectangle = 2(l + w)
where
l = lengthw = widthTherefore,
perimeter = 68 m
68 = 2l + 2w
l + w = 34
l = 34 - w
Hence, the largest possible area is at the amximum.
area = lw
area = w(34 - w)
area = 34w - w²
The maximum is at dA / dw = 0
Therefore,
34 - 2w = 0
2w = 34
w = 34 / 2
w = 17
l + w = 34
l + 17 = 34
l = 34 - 17
l = 17
area = 17² = 289 m²
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of these four causes of death due to injury
Answer:
Injury on the neck can be fatal, as well as injury in the spine, head, and any other major injury such as a broken rib, which has possibility to damage other organs.
complete the diagram of the mechanism of a general enzyme-catalyzed reaction. the abbreviations e, p, and s indicate the enzyme, product, and substrate, respectively.
It should be noted that the the mechanism of a general enzyme-catalyzed reaction. the abbreviations will be E + S = ES = EP.
What is an enzyme?An enzyme simply means a substance that acts as a catalyst that speeds up the rate of chemical reaction.
In this case, it should be noted that the the mechanism of a general enzyme-catalyzed reaction. the abbreviations will be E + S = ES = EP.
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Suppose a flask is filled with of , of and of. the following reaction becomes possible: the equilibrium constant for this reaction is at the temperature of the flask. calculate the equilibrium molarity of. round your answer to two decimal places
The concentrations of the species at equilibrium is obtained from the ICE table.
What is equilibrium constant?The equilibrium constant shows the extent to which a reactant has been converted into products. A large equilibrium constant means that most of the reactants are converted into products The question is incomplete as the details as missing.
However, for a hypothethical reaction; nA + mB ⇄ xC + zD, the equilibrium constant is obtained from; K = [C]^x [D]^z/[A]^n [B]^m. The concentrations of the species at equilibrium is obtained from the ICE table.
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List down 3-5 potential obstacles you may encounter on work immersion
(WILL MARK BRAINLIEST!) If a student attends a non-credited high school, or in their case a homeschooling program, will they have to take the SAT/ACTs to be able to attend community college? Please answer explaining how a student such as this can get into college and the requirements they would need.
Answer:
So I turned homeschool not too long ago and you do need to the the SAT/ACT depending on which community college it is? If the high school or college offer ACT then the test you most likely need to take is the ACT. But if the test they offer is SAT then you should take that. Taking both of the SAT and ACT would only do better on your resume/aplication so it's really up to you. I plan to take both if I have the time. But I heard most people take the ACT. You should check what your community usually offer.
Hope this helps.
Explanation:
Answer: college admissions is handled very similarly for homeschoolers as it is for traditionally schooled students. In fact, many admissions offices actively seek out homeschoolers. Admissions officers evaluate each student within the context of his/her own background and the opportunities they've had. There are, however, a few differences regarding how homeschoolers submit certain application materials. As a homeschooled student, your parent or primary teacher is responsible for creating your high school transcript and for sending it to your colleges. Parents have a few different options for going about this:
1. Working under an umbrella school that produces official transcripts and diplomas
2. Creating their own transcript and diploma
3. Enlisting a service that specializes in transcript and diploma creation
4. Joining a homeschool group that produces professional transcripts and diplomas
Explanation:
Your transcript should include all of the following information:
Your name, the name of your homeschool (if applicable), address, and phone number
Your high school course list ordered by year (grades 9-12)
The institution where each class was taken (i.e. homeschool, online institution, community college)
The grade scale being used in your homeschool
Your overall GPA
Credits given per course (listed per semester and per year)
Expected graduation date
Parent signature with a date
Homeschoolers do not need a GED or a diploma to apply to college or qualify for financial aid; you just have to declare that your homeschool education meets state law requirements. Most homeschooled students choose not to take the GED if they have valid transcripts, as colleges will place the most emphasis on your transcript and standardized test scores. If you’re homeschooled through an online academy, virtual school, or organized homeschool program then they will award your diploma according to their own standards. If you’re homeschooled independently by your parents, then your parents have the option of issuing you a diploma if your transcripts indicate you’ve met the basic state requirements for graduation. When filling out the FAFSA, be sure to check “homeschooled” when it asks for your high school completion status. Even if your homeschool is administered through an umbrella organization, you should still check “homeschooled” instead of “high school diploma” to avoid any delays in the processing of your application.
