4) For each of the improper integrals below..... • Re-write the integral using the correct limit notation. • Evaluate the re-written integral as we did in class. 1 (@) : | xln(x) dx |, tan(x) dx dx (b)

Q: In the integral of x cos 2x dx with limits form 0 to pi/2, what is the indefinite integral? Select…

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Q: For the integral x cos. X cosx dx

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Q: 5. Find the definite integral of: a) fr (2cosx – 3sinx)dx

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Q: 9. Find the integral, using u substituti x-(1-3x²)*dx a.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

Q: '1 1 Given that x² dx = use this fact and the properties of integrals to evaluate (8 — бх2) dx.

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Q: Find a value for n to ensure that the absolute error in approximating the integral x cos x dx by the…

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Q: Evaluate the improper integral: e-X dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: A. Evaluate the following indefinite integrals using the Power Rule: 1. SE Va dx 2. S dx 3. S(-Vx +…

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Q: Evaluate the improper integral 1 dx x - 1

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Q: Evaluate the improper integral if it exists 1 dxp:

A: We have to use properties of integration.

Q: 2ea dx (ет — 1)2 1

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Q: 4 1 : Evaluate the following improper integral by using proper limit notations: dx. (4 – x)2/3

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 3. Evaluate the double integral /sin(x+y) dx dy by using Simpson's 1/3-rule with four sub-intervals.

A: I = ∫0π2∫0π2sin x+ydxdy,

Q: 3. Prove properties (3) and (4) analytically, by making x = -t in the part of the Integral from -a…

A: Concept:

Q: (b) Evaluate 1 (x-2)¹/3 dx by using properties of improper integrals.

A: b Given integral is ∫131x−213dx. We have to evaluate the given integral by using properties of…

Q: What is the integral of sin^5 x dx if the lower limit is O and the upper limit is T/2?

A: We have to find out

Q: Find the integral of 12 sin^5 x cos^5 x dx if the lower limit is O and the upper limit is T/2.

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Q: 3. Evaluate the integrals √tanh x sech² xdx

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Q: so xe x dx

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Q: Evaluate the integrals.∫(x/(x-2))dx

A: Solution -  Given Integral is -  y = ∫xx-2dxWe can write it as - y = ∫x-2+2(x-2)dxy =…

Q: 4. Evaluate the definite integral by using substitution. x-1 dx (x+ 2)2/3 -1

A: given the definite integral is∫-16 x-1(x+2)23dx

Q: Evaluate the indefinite integral: 3 dx J x In(5x)

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Q: Evaluate the improper integral e-1/x dx

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Q: Find the indefinite integral. S-x² + sin x – 3* dx | In |x| – - 3* + C COS X - 3 In 3

A: detailed solution is given below

Q: 19. Use Simpson's rule with n=8 to estimate the following integral. Estimate your error. So5-4 cos.x…

A: Given integral can be evaluated by using Simpson's rule with n=8 as shown below

Q: Find the indefinite integral.

A: To find: The indefinite integral ∫dxxln x23. Concept used: Power rule of logarithmic: ln ab=b·ln a…

Q: Evaluate the integrals ∫ ln x/x3 dx

A: Evaluate the integrals  ∫lnxx3dx

Q: Approximate the integral from 1 to -3 of e-x dx using four equal subintervals.

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Q: Evaluate the integral of 2x/(2x^2 + 4) dx if the upper limit is 6 and the lower limit is 3.

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Q: set up an integral ....bounds x=3pi/4 x=-pi/4 y=-sinx and y=-cosx

A: GRAPH

Q: Evaluate the integral using the methods covered in the text so far:                    ∫ (7 − e10x)…

A: Here we have to evaluate I=∫(7-e10x)dx

Q: 1. Find the values of the following improper integrals with unbounded domains of integration, if…

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Q: 13. x-x dx x² +x?

A: We need to evaluate the integral ∫13x-x-3x2+x-2dx ................ (1)

Q: Evaluate the integrals ∫cos 2x dx

A: We have to evaluate the integral: ∫cos 2x dx In this case we do use substitution method so assuming,…

Q: Q5. Apply the mean value theorem for integrals to evaluate e Lim -dx. 2 + CoS x

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Q: Evaluate the integrals

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Q: Evaluate the integrals ∫ ln x/x2 dx

A: Evaluate the integral ∫lnxx2dx.

Q: 5 Only one of these calculations is correct to evaluate the definite integral 7x In(x) dx Using the…

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Q: 4. Determine the following integrals 4.2 - dx - a x

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Q: Jcos(2x)+ sin(0.5x) Using riemann compute for the integral of F(x) = tan(3x) sum over the interval…

A: We can solve this using Riemann sum

Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: Evaluate the improper integral. x In6x dx 0.

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Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

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Q: dx (4 + x²)²

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Q: -3 evaluate the integral (x2 – x + 2) dx using its definition.

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Q: 5 Only one of these calculations is correct to evaluate the definite integral x² In(x) dx 1 Using…

A: First we have to find h and it's corresponding formula.

Q: 2 Evaluate the improper integral e4z dx, if exists. a) The nature of the integral is:

A: Explanation of the solution is given below...

Q: 3. Evaluate integral by using a basic substitution: S x² sin xdx

A: Given: ∫x2sinxdx To evaluate: The given integral.

Q: 7 Evaluate the improper integral, if exists : dx (5 – x)3

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