(4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

Q: -Find the value of th integral e-x' dx.

A: Consider I = ∫0∞e-x2 dx                              (1) Let x2 = t On differentiating both sides,…

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Q: 3. Find the following definite integrals. (2x +3)dx (x2- 1)dx x² - 2x)dx sin(3x + 4) dx 1

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A: We have to find the indefinite integral

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A: Here first put x=1/t and then the expression inside the square root as y^2. As showing in solution

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Q: Q: Find the integration for the following functions: - 1.- °(1-cos2x) 2-5 2- sin(tnx) dx 3-f-…

A: According to the guidelines issued by the company we are supposed to answer only first three sub…

Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: 3. Find the indefinite integral: Sx(x-2)* dx

A: Please rate

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A: To evaluate

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A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: Find the indefinite integral. 1. 16 + t² dt * (x² + 4)³/2 + 4)3/2 2. -dx-

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: 1 7. Evaluate the integral -dx using Simpson's method and also find the error comparing ó x +9 with…

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Q: 2. Consider the problem of evaluating the value of the definite integral 2х-п dx . sin(x) i) Apply…

A: According to the Given question; I=∫022x-πsinxdx Ans 1; By Monto Carlo Method; I=∫022x-πsinxdx…

Q: 7. Evaluate the improper integral. -kx e (k: constant)

A: Please refer to the image below.

Q: 3 Evaluate the integral: dx 2 Vx -1

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Q: 33 Vx2 f(x) = + Ve2x + 2x – In e, x # 1 TT Sin 2x - 1-x

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Q: S°(xe* + 1)dx

A: In this question we have to solve the given integral by using some of the newton-cotes rule.

Q: =dx V2x* +3 4

A:

Q: 3 Evaluate the integral |x V2x +1 dx ?

A: ∫x22x3+1dx We need to integrate the given function.

Q: Q-3: Find the general indefinite integrals of: 1. S cos ntcos(sin(at)) dt 2. SVx +2x dx s dx 3-2x2-4…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate the definite integral. ∫(lower bound=π/4)(upper bound=0)sin(4t)dt

A: Given,             ∫π40sin4tdt

Q: (9) Evaluate the indefinite integral f X+2 dx x² + 4x 2

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

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Q: 5e3* dx J 6. 9-12e3 +4e6x

A: integration

Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

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Q: 6) Use the successive approximations method to solve the following Volterra integral equation: 2 и…

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Q: x² – 25 dx Jx+5

A: Formula: a2-b2= (a+b)(a-b)

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A: topic - integration

Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

A: Solution of question as follow

Q: 15 Find the integral | 2/x (1+x) dx.

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Q: 1. Evaluate the integral 2 dx x2 +4x + 20

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Q: 6. Evaluate the integral e* dx ex + e-x

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Q: |(16x3 - 3x2 + 4) dx (16х3

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Q: 2. Use integration by parts to establish the reduction formula: Sx" cos x dx = x" sin x – n x"-1 sin…

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Q: 2. Evaluate the integral x(3 – 5x) (3x – 1)(x – 1)2 dx

A: To solve the following integral

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A: Given problem:-

Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

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Q: 1) Evaluate. Јx cosh ax dx 2) Evaluate the integral. (In x)² dx x3 1

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Q: (2x+5)² What should be the rewrite of the integrand of S x² dx so that the resulting integral is…

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Q: 10. Find the indefinite integral. x – 2 dx x² + 1 -

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Q: 5. Evaluate the definite integral (1+lnx)² dx а. 1 dx. b. -1 2x+3

A: Explanation of the answer is as follows

Q: 1. Evaluate the integrals that converge: dx 2x ! dx (x2 + 5)3 b) a) 3-x - 00

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