Evaluate the integral. - {i-* S2 14 - x2 if -3 sx s0 f(x) dx where f(x) if 0< x s 2 -3

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Q: Evaluate the integral. 4 f(x) dx where f(x) = if -3 Sx 0 0 <x < 3 6 - x2 if

A: we have to find the following integral

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A: Since multiple questions are asked I am answering first question

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A: Here we have,

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Q: [(b) find the integral in the interval [1,4] S(3/2 sqrt(x)-4/x^2) dx ].

A: To evaluate the given integral on [1,4]

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Q: Evaluate the integral / f(x) dx, where -1 -{ if – 1 < x < 0 if 0 < x < 1 -X - f(x) = 1-VT - x²

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Q: b)does the integral converge 2x-2 dar (r+1)(x²+1

A: Consider the given integral. I=∫1∞2x-2x+1x2+1dx Now, find the partial fraction of the function.…

Q: Evaluate the integral. La S4 5 - x2 if 0 < x < 4 if -4 sxs 0 f(x) dx where f(x)

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Q: 3. Prove properties (3) and (4) analytically, by making x = -t in the part of the Integral from -a…

A: Concept:

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Q: Evaluate the integral. S. 4 x* - 3 dx 14 4 x* - 3 dx = 14

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Q: Evaluate the integral. if -4 < x s0 0< x < 3 3 4 f(x) dx where f(x) 15- x2 if

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Q: Evaluate the integrals ∫x-4/3 dx

A: Given information: The integral is ∫x-43dx. Calculation: Use the power rule of integration…

Q: Evaluate the integrals ∫ x dx/9 - x2

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Q: determine whether the improper integral converges and, if so, evaluate it.

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Q: Evaluate the integral 1 -dx. 2Va(x + 1)

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Q: S x³et*dx

A: A detailed solution is given below

Q: Find the integral

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Q: Determine if the integral converges or diverges by comparison.

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Q: Determine whether the improper integral converges and, if so, evaluate it.

A: ∫56dxx-532 On integrating, we get ∫56dxx-532=∫56x-5-32…

Q: Evaluate The Integral

A: Given function is

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

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Q: Evaluate the integral. S2 15 - x2 if o < xs 3 3 if -3 sx S0 f(x) dx where f(x) = %3D

A: See step 2

Q: a. Evaluate the integral and state if it converges or diverges ∞∫0 ex / (1+e2x)

A: ∫0∞ex1+e2xdx=let u=ex    du=exdxif x=0   then u=e0=1if x=∞ then u=∞…

Q: -0o (x2 + 1 Evaluate the integral if it converges. Enter the exact answer, or enter na if it…

A: The given integral,      ∫-∞+∞xx2+12dx

Q: Evaluate the integral.

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Q: Evaluate the integral. S3 15 - x2 if 0 < x s 3 if -3 sxs 0 f(x) dx where f(x)

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Q: determine whether the improper integral converges and, if so, evaluate it.

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Q: Evaluate the integral. [4 f(x) = | 16 – x² if 0 < x < 4 if -4 sxs 0 f(x) dx where

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Q: Evaluate if the integral converges 1. 1. dx (x-1)7 , sin x dx 3. dx 2.

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Q: Evaluate the integral. S4 15 – x² if -4 < x < 0 f(x) dx where f(x) %3D -4 if 0 < x < 2

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Q: 2. S*3*+2 dx x+2

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Q: determine whether the improper integral converges and, if so, evaluate it.

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Q: dx x (In x)5

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Q: determine whether the improper integral converges and, if so, evaluate it.

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

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