4. Evaluate the integral sin x cos x dx by two methods: first by letting u = sinx, and then by letting u = cosx and then explain why the two apparently different answers obtained in part (a) are really equivalent. 5. If you want to evaluate an integral by u-substitution, how do you decide what part of the integrand to choose for u?

Q: Еxercise: 1- Use the Composite Trapezoidal rule with the indicated values of n to approximate the…

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Q: on 3.2 p. 283/285 # 90 pute the following integrals using the guidelines for integrating powers o…

A: Please refer to the image below

Q: 18 Estimate the error if cos t is approximated by 1- 2 in the integral cos t? dt. 4! - -+ The error…

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Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: Choose among the following suitable to define the given integrations: Sx sin x² dx By parts, the red…

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Q: 7. Express the solution of y" + 2y' + 2y = sin (3t) convolution integral (you don't need to evaluate…

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Q: 2.Find the following indefinite integral without substitution. S sec y (tan y- sec y)dy

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Q: 3. Solve the integral by two grid in the y-direction and four grid in the x-direction with…

A: Solve the integral by two grids in the y axis and four grids in the x axis with Trapezoidal rule:…

Q: In this question, you are asked to investigate the following improper integral: XPs- 10.1 Firstly,…

A: Since you have asked multiple questions, we will solve the first three subparts for you. If you want…

Q: 5. Evaluate the indefinite integral. S cososin'oc (1) (3x - 2)20 dr (2) (3) S etanr sec?rdr

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Q: Find the value of the definite integrallo 2 cos ( x ) dx given that the antiderivative for the…

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Q: 7) Evaluate the integrals a) 3(x + 1)²dx b) secx (tanx +cosx )dx

A: An indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that…

Q: Evaluate the integral. n/2 | [2 cos ti -3 sin 5t j+ sin? 3t k] dt 0. n/2 | [2 cos ti- 3t k dt = cos…

A: Integrate

Q: For each of the improper integrals below, if the comparison test applies, enter either A or B…

A: given 0<e-x≤1  for x≥1 1) ∫1∞5+sinxx-0.3dx it is known that  ∫1∞5+sinxx-0.3dx≤∫1∞5+1xdx…

Q: Estimate the error if cos t² is approximated by 1 integral , cos r² dt. 4! in the 2

A: We have,

Q: 13. If u(x) = sin 3x and v(x) = x, what are du and dv? Writedown  u dv and  v du in this…

A: Given- ux=sin3x and vx=x To Find- The value of du and dv, write down the value of ∫udv and ∫vdu,…

Q: Evaluate the integrals ∫cos (1 - ln y)/y dy

A: We have to find the integrals: ∫cos1-lnyydy We will find this integrals by substitution method Let…

Q: 1. Prove that L{cos(at)} cos(at)dt integrating by parts twice and the evaluation of the improper…

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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: Find the Lebesgue integral fio.11 f, where f(x) = x. Note: although this can be done by various…

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Q: 4. Evaluate the definite integral_ TC 3. sin(3t) dt 0.

A: Explained below

Q: Identify an analytic anomaly why numerical integration formulas will fail for J_11-x² sin(ax) dx.…

A: Given integral is∫-11sinπx1-x2dx

Q: 1. Evaluate the integral using FTC Part 1. | (23 – 2a) dæ 2. Evaluate the integral using FTC Part 2.…

A: As per guideline we have to solve only one question

Q: 1) Evaluate the integrals: (a) f sin³ (2x) cos (2x) dx (b) sin³ (2x) cos (2x) dx

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Q: Use Simpson rule' 1/3 Method with (n = 8) to estimate the integral: f(x) : e^(sin 9x), where a = 0 &…

A: Given; f(x) = e^(sin 9x) and n=8 And a=0 , b=10

Q: %23 %24 In using the technique of integration by parts, you must carefully choose which exp…

A: Given ∫x7 cos(8x)dx

Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

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Q: , 1. Take the following integral numerically using an end corrected method. (n-7, h=0.001) (give…

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Q: 5. Evaluate the integral. (Use C for the constant of integration.) sin³ (y)cos (y)dy

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Q: 1. Find the exact value of the iterated integral by changing the order of the integration: 8 2 1…

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Q: 11 Let I= [[5 sin(v')cydx . By reversing the order of integration of I, we get:

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Q: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

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Q: Evaluate the integral / cos (r) sin(x) dx 16 COS using the substitution u = cos(x). ,16 cos" (x)…

A: This question is based on indefinite integral.

Q: 1. Set up the following improper integrals by definition. sin(x) xe-x³ dx dx 2? — Зх — 4 а. с. 7 et…

A: Solution b: Given integration is ∫17exx-1dx Here 1 is the only point of infinite discontinuity So we…

Q: Depending on the real parameter p and q, what can you say about the result of the following im-…

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Q: 3+n (2x) dx By specifying the +ype of examine it by explainings conveyere integral, x --

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Q: 9/u The evaluation of the Integral of S° sin2x cos4x dx is

A: we have to integrate

Q: Evaluate the integral. (Use C for the constant of integration.) 3 cos x dx 6 + sin x

A: Evaluate the integral.

Q: 3. Change the order of integration sin dydx. Hence, evaluate the integral. y

A: Sol ∫0π∫xπsinyydydxChange order of integration =∫0π∫0ysinyydxdy

Q: 1. Evaluate the trigonometric integral. (1) [20sin² (2x)cos (2x)dx (ii) S4ta dt

A: Given integral is: I=∫20sin22xcos22xdx To solve this integral we will use the following…

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

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Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

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Q: 1. Use the table of integrals to integrate the followin a) S sin ) s in () dt

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Q: 2 S sin (ax)cos(ax)dx

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Q: Suppose we want to integrate by parts the integral -sin(2x)dx. Which function should we choose as…

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Q: Select the improper integrals in the following list of definite integrals. 2 7dt o 1-t2 1 9x In(x)dx…

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Q: Only one of these calculations is correct to evaluate the definite integral Vx+1 dx Using the…

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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: 1. Evaluate the iterated integrals. √27x² (a) [sin - dydx (b) √√x² - y² dydx

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Q: 5. Use integration to find the exact area outside r = 4 cos 0 and r = 4 sin 0 but inside r = 2.

A: