1. Evaluate : S (4x* + dx 2 S"(4x³ +)dx 0. x+1

Q: Evaluate the integral 3. 2х dx х2 — 4

A: Will use substitution to find this integral. Substitute x square - 4 is equal to t.

Q: Evaluate the integral. 停。 2 - 4 dx 8

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Q: Evaluate the integral. x³ + 4 - dx (x + 4) (x + 3)

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Q: What is dy/dx of 1/2e^2x

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Q: +1 dx. (x+3:2-5)3

A: To evaluate  ∫x2+1x3+3x-53dx

Q: 3 2 dx . 3

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Q: Find

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Q: Evaluate the integral x3 + 39 dx. + 4x + 3 x2

A: Try to simplify the numerator in terms of the denominator.

Q: Evaluate the integral x dx. -4 3 |x| dx =] -4

A:

Q: 14.Use a substitution to evaluate / aVx+1 dx rVa+1 dx. Show all details of the process.

A: To solve- given integral by substitution  method.

Q: 5x-1 dx 2x+3

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Q: Evaluate the integral. dx =, x>6 x - 36 dx x²x - 36

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Q: Use the Midpoint Rule with n = 3 to approximate the integral 16 | (- 10x + 2x2) dx 10

A: In this question we will use basic of calculus i.e concept of midpoint rule to approximate the…

Q: Evaluate the integral. бх + 2 dx = | x2 + 2x – 3 -

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Q: Use u-substitution to evaluate the integral: x/(x+2)^3   dx

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Q: Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

A: ddxln kx=ddxln x, where x>0 & k is a positive real number.

Q: Evaluate the integral. '5 dx (x2 - 1)3/2

A: *Given integral is, I=∫251x2-132dx Integrate the above expression. I=∫251x2-132dx Put,…

Q: Evaluate the integral: / (3x+5)dx x²+2x+1

A: ..............(1)

Q: Evaluate the integral.

A:

Q: Use substitution to find the indefinite integral.

A: Integration by substitution is a method to solve integrals line in the above question where the…

Q: Evaluate the integral. 2x´dx 4 5.

A: ∫452x2dx

Q: Evaluate the integral. 3 x - 3 dx 11 X

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Q: Evaluate the double integral : 8. dy dx 88 -

A: We have to evaluate the given double integral   The given expression is

Q: Evaluate the integral. 1/2 2 - 4x + 1 dx x² – 3x +2

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Q: Evaluate the integral. х3 — 5х — 8 dx x2 — х — 6 -

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Q: Evaluate the integral. 2 x²-5 dx 8 2 X 8 X X -5 dx=

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Q: (y5 – x²e») dx dy -11-3

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Q: 5. Evaluate x + v1 – x² dx by interpreting it in terms of areas.

A: We have to consider it as sum of two functions.

Q: Evaluate the integral. 7x - 6 -dx (x+4)(x² + 1)

A: We have to find solution

Q: Evaluate the integral. 0.4 x2 dx 4 - 25x2 |

A:

Q: Find the integral

A: Given:              ∫x8-x32dx apply u-substitution: u=8-x⇒du=-dx           =∫--u+8u32du take the…

Q: Use substitution to find the indefinite integral.

A: Given integral: ∫x2-6xx-3 dx Substitute u=x2-6x and differentiate it w.r.t 'x'…

Q: (x-1)* dx

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Q: Evaluate the integral. 3 dx -2

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Q: 5 一=A+hxsl-x dy=?

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Q: Evaluate the integral. '5 x - 4 dx x2 - 3x - 18

A: We first factor the denominator. ∫-25x-4x2-3x-18dx=∫-25x-4(x-6)(x+3)dx

Q: evaluate using the appropriate method or combination of methods.

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Q: Evaluate the indefinite integral -dx x4 + 3

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Q: 8) Evaluate the Integral x2 + 2x dx

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Q: 3x dx x +x-6 2

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Q: Find the integral [(3x² – x) In(3x)dx .

A: Given query is to solve the integral.

Q: Find the indefinite integral. dx | 7x2 +2

A: Given, I=∫x7x2+2dx

Q: Evaluate the integral. 12x – 9 - dx = x2 + lx – 6 4 -

A: Given, Evaluate ∫4512x-9x2+1· x-6dx

Q: What change of variables would you use for the integral  ∫(4 - 7x)-6 dx?

A: Consider the following integral: I=∫4-7x-6dx Substitute 4-7x=t→-7dx=dt→dx=-17dt in I:…

Q: 2 Evaluate the integral: 3x(5-3x dx

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Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

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Q: Evaluate the integral. 3x dx 3* +4

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Q: 16. Evaluate x + v1- x² dx by interpreting it in terms of areas.

A: