a. Use a computer algebra system to evaluate the following integrals. i. xe" da i. x² e" dx ii. iv. dx dr 4.

Q: Rewrite each of the following triple integrals in the indicated order. 4-x 12-За-6у (a) / dz dy dx…

A: a) Given integral is   ∫04∫04-x2∫012-3x-6y4dzdydx we have to change the given order of integration…

Q: Evaluate the given integral using the substitution (or method) indicated. (x+ 9)e*+ 9) dc; u = (x+…

A: Given inlegral ,                       (x+9)2 I = ∫ (x+9) e            dx

Q: Which among the following is an improper integral? In3 ex In2 4- ex 1 dx X/16 - Inx 1 dx x Inx In2 1…

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Q: Evaluate the integral, if it exists.  ∫01 y2 √(y3 + 1) dy

A:

Q: et dx e – 2e*

A:

Q: b) Evaluate the integral by parts. S, x* Inx dx

A: given I= ∫1ex4 ln x dxby using LIATE rule we can rewrite integral as    I= ∫1e ln x   (x4) dx     =…

Q: Evaluate the integral, if it exists.  ∫01 y (y2  + 1)5 dy

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Q: 14 Find the integrals using integration by parts. a. fx(x + 4)°dx c. fr'e"dr

A: As per our guidelines I am solving only first three parts of the question please resubmit the other…

Q: t² – n/i + Vt csc(t) TTVE dt

A: Given: I=∫t2-πt+t  cosecttdt

Q: Evaluate the following integrals. xdx |Ja +3 а. b. z · 3*dz | VI (2 – x)² dx с.

A: Let's find.

Q: Tπ L2 sin3xdx Tπ 4

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Q: Evaluate the integral. x sec? (7x) dx + C

A: We have to find integral.

Q: Evaluate the integral by substitution a) "x sin(x?) dx

A: Given : ∫0πxsinx2dx

Q: Evaluate the following integrals: 1 = fx'e* dx 1. I

A: Given : Inetrgal equation is given

Q: Evaluate the following integrals Sa 4 |(x? + 4vz - - 6)dx x3

A: To solve integration of such type. You just need to integrate individual terms separated by either +…

Q: Use the Table of Integrals to evaluate the integral. e70 sin 60 de

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Q: Evaluate the following integrals.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: For what values of a is each integral improper? Explain.

A: (a) consider the integral ∫a5dxx+2.

Q: Calculate the following integrals. (a) ſ 4 dx (b) S,". 100 1 - dx (c) z dx

A: (a) ∫-134dx⇒4∫-13dx⇒4x-13⇒4(3-(-1))⇒4(3+1)⇒16∫-134dx=16

Q: Use Gauss-Legendre formula to evaluate the integral e¯x*dx_with n = 3.

A: Evaluate the integral          ∫01ex2dx using Gauss-Legendre formula with n=3.

Q: Evaluate the following integral: Stan x sec³ x dx

A:

Q: Find the values of the following Integrals: ii) S sinx tan'ccord dx ü) Sex uci+ e* ) dze in) St…

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

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Q: Use the substitution formula to evaluate the integral. dx 1. 22 11 11 O00

A: Solving the problem by substitute method.

Q: Evaluate the integral. x sec?(8x) da +C

A:

Q: S tan?xsec³x dx

A: To evaluate the following integral.∫tan2 x sec3 x dx

Q: Evaluate the given integrals. 4. J(secx + tanх)? dx

A: Given problem:- ∫ (tan(x) +sec(x))2 dx

Q: Evaluate the following integrals by using the substitution u= 4x+ 1. %3D (a) 4x + 1) dx. (b) 4.x+1)2…

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Q: A. Evaluate the following integrals by substitution. 1. Sx(2x? + 3)®dx

A: Put (2x2+3)= t  Differentiating both sides  4x dx= dt

Q: Evaluate the integral by making the given substitution. xV+ 14 dx + 14 dx, u = x3 + 14

A:

Q: Evaluate the following integrals // a dA R= {(x, y)| 0 < r < 1, –x <y < x} 3r2 +1 R

A: Given, ∫R∫(y/(3x²+1)) dA 0&lt;=x&lt;=1 -x&lt;=y&lt;=x

Q: 6 sec*x dx

A:

Q: x+1 dx

A: We need to integrate∫x3+1xdx

Q: Calculate the following integral, La CUP x6 (x4 + a4)² a4 ) 2 dx, (a > 0).

A: In the given indefinite integral. The method of substitution is used to simplify the integrand.…

Q: Evaluate the integrals: x-y х-у (x+y)3 dxdy (x+y)³ kpxp I xpáp S pue Are the results the same? Why…

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Q: calculate the following integrals, assuming fCx)=ユ) fx)dx=7 f(x)dx= %3D

A: ∫01fxdx=1∫02fxdx=4To find:∫12fxdx

Q: ^ du 1 1+2 Sinn

A: Solving the given integral using the substitution method Also using the formula for the integration…

Q: Which of the tollowing integrals gives the ength of the graph y=18 between X= a and a. a 1X2+X dx b.…

A: We have to find the length of the graph  y=x  between x=a and x=b where  0&lt;a&lt;b.

Q: Evaluate the integral

A:

Q: O Evaluate the integrals Jscx+y+2?s da dy dx-

A: according to the guidelines we should have been able to do only one question at a time #1-a

Q: L'²₁ (r + 1)² dr

A:

Q: correct answer to evaluate the following integral dx Jo (1 - x*)2

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Q: 1 (a) . Ta – 2)3/2 dr. e1/z dr.

A:

Q: Evaluate the following integral (a – /(x² + y²))dA Jxz+y?sa²

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Q: Evaluate the integral. 5 x2 e dx +C

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Q: b) Calculate (i) the following integrals x² (3x³ + 2)²dx

A:

Q: esin(e")dx 8 cos (e*

A: Evaluate: ∫exsinexdx8cos2ex

Q: Which among the following is an improper integral? In3 ex xp- |4– ex In2 e 1 X/16 - Inx e 1 x Inx…

A: Improper integral :It is a definite integral . There are two types of improper integrals :- First…

Q: 7. fx² cos mx dx, where m is constant.

A: We have to solve the integral

Q: Use the value of the first integral I to evaluate the two given integrals.

A: ∫01x3-2x dx=-34