Evaluate the integral Jo 76+1 dx, using Residues:

Q: Evaluate the integral from pi/6 to pi/3: ∫csc3x dx

A: ∫π6π3csc3(x)∫π6π3csc2(x) csc(x)dx Apply integration by parts formula Let u=csc(x) du=-cotx csc(x)…

Q: Write the integral in terms of u and du. Then evaluate:                                       ∫…

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Q: J Sin (In 6) de

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Q: Evaluate the integral. 8x /1 – x² dx - NOTE: Enter the exact answer.

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Q: Evaluate the integral. 8 dx 3 1

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Q: evaluate the integral.

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Q: Evaluate the integral. 43tan“x - secx dx %D

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Q: Evaluate the integral. 1/2 Jo 7 cos-¹(x) dx

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Q: x In(2 + x³) dx

A: Topic  = Integration

Q: Evaluate the integral by making the given substitution. dx u = 7x + 8 (7x + 8) '

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Q: Evaluate following integral: 2dr (7²+1)(x+1)²

A: The given integral is: ∫2dx(x2+1)(x+1)2 First, we need to decompose the expression 2(x2+1)(x+1)2 by…

Q: Evaluate the integral. du 2

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Q: Evaluate the integral.  ∫ (8 − 9x) dx __________________+ C

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Q: Evaluate the integral (1² – 4z) dz using its definition.

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Q: Rewrite the integral using substitution: 3 ₁³ (x² cos(4x³)) dx

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Q: Evaluate the integral. '1 (x14 Jo + 14*)dx

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Q: Evaluate the integral or state that it is "divergent" -5 х — 2 dx х2 +x — 6

A: From the given problem: I=∫15x-2x2+x-6dx So, we can also write as:…

Q: Evaluate the integral. 6 dx 16

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Q: Evaluate the integral: Jo Sí(3xyY+ 5) dy dx Answer:

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Q: Evaluate the integral by making the given substitution. [sec (3x)tan (3x)da, u = 3x +C

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Q: 6z* cos (r*) dr-

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Q: Evaluate the integral by making the given substitution. sec(2x)tan(2x) dx, 2x +C

A: Solving the problem by doing the integration.

Q: Evaluate the integral. 2x² e" dx%3D

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Q: Evaluate the integral. (11 - t)/e dt

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Q: Use the substitution a = 7 tan(0) to evaluate the indefinite integral 85dx 49 +C

A: We have to find

Q: Evaluate the integral. (6х — 9) dx Jo

A: objective is to evaluate the integral

Q: evaluate the integral.

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Q: fco | cos 5xsin 5xdx

A: SOLUTION-

Q: Evaluate the integral using the trigonometric substitution x =2 tan0 . x3 %3D dx x² + 4 Vx²

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Q: Consider the integral dx x . Using u-substitution, what is an appropriate u and du? -2x 2e

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Q: Use the indicated substitution to evaluate the integral. 1 dx, x = 15 sec(0) xVx² – 225

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Q: Evaluate the integral. 49 9Vx dx J25

A: Given: I=∫25499xdx we know that ∫xndx=xn+1n+1+c

Q: Use the Table of Integrals in the back cover of Stewart's text to evaluate the integral -1x4 dx Vx10…

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

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Q: Evaluate the integral by interpreting it in terms o 0. 9 - x2 ) dx -3 9 3 + 4

A: ∫-30 (3+9-x2)dx=∫-30 3dx+∫-30 9-x2dx                                    =A+BA:∫-30 3dx=3x|-30…

Q: Write the integral in terms of u and du. Then evaluate.

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Q: Evaluate the integral by making the given substitution. sec(4x)tan(4x)da, u = 4x + C

A: To find following integration  I = ∫ sec(4x).tan(4x).dx

Q: By using Simpson's Rule, calculate the integral 2r +a?dr.

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Q: Use the Rectangle Property to evaluate the following integral. -3 (-14) dx = %3D

A: given integral :

Q: Evaluate the integral by making the given substitution. sec(4x)tan(4x)dx, u = 4x + C

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Q: Evaluate the integral

A: Given: ∫00.6x29-25x2dx

Q: Evaluate the integral using FTC I.

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Q: Use the Rectangle Property to evaluate the following integral. -5 (-13) dx 10

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Q: Evaluate the integral f v96 + 16x² dx using trigonometric substitution.

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Q: Evaluate the integral. • T/4 sec*0 tan40 de

A: Given :

Q: R sec" (82) daæ

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Q: 36" dx o V6 + 3

A: We have to find out