a) Let f(x) = 3x² + 2x – 3x-1 +72". Compute the integral of f. = x-1 and let h(x) = x² + 2x. Compute the integral of 7h(x) + b) Let g(x) 4g(x).

Q: In Exercises 29-76, evaluate the indefinite integral.

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A: We'll use the Maclaurin series expansion for e^(x^2/2).

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Q: Evaluate the integral: Jxe dx хе -2x -xe -Xe 2x +C -Xe2x e -2х —хе +C 4 Xe 2: -2x хе -2x e +C -2x…

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Q: Let f:[0,7] be defined by f(x) = x2-3x+1. Let a(x) = 3I(x-1) + 2I(x-4) + I(x-5) + 4I(x-6), where I…

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Q: 4- 2x Evaluate the following integral : dx 2x +4,

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Q: (2x3+9)dx 2. S (x2+3)(x²-2x+3)

A: Given that

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Q: Evaluate the integral.

A: Given integral: ∫121241-x2dx

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A: Answer and explanation is given below

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A: As per our guidelines we can solve only three sub parts at a time. Please repost unsolved part…

Q: The particular integral of (D² – 2D+ 1)y = xe® is 2 -2et - x2 3

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Q: 9 Evaluate the integral f 2x (x² + 1)° dx using the substitution = x² + 1. и — с 2.x (x? + 1)° dx +C

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Q: Evaluate the integral f 2x (x² + 3)° dx using the substitution u = x2 + 3.

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Q: Evaluate the integral. 7 √49-x² √49-x²-22 49-x² 1 √²-3³ (x² + y² + 2²)1/2 dy dz dx =

A: Solution:-

Q: a) Let f(x) = 35 – 2a-1 +5+ 7x². Compute the integral of f. %3D

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Q: EXERCISES 7.3 Evaluate these definite integrals. dx Vx+2 1. -5 dx Vx – 1 2. 3. 3x²e*³dx

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Q: Find the integration distance (f, 9) = | f(x)g(x) dæ between the given polynomials. f(x) = 11æ – 3,…

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Q: 7. Evaluate the integral r8-2x (x + y + 1)-2 dydr.

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Q: Evaluate the integral dx 2x리x-3월 x2 1 3 + V2x In A + C 2/3"3 - V2 | ® In(2x x - 3{x²) +c 1 In + C…

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Q: 1. Use integration by parts to find the integral below. In(x19)– 9x10+C a. b. x ·In(x1)– 10x10+ C c.…

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Q: 5x dx. - 6 Compute the integral x2

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Q: (5x° + 4x + Ix Consider the indefinite integral dx x2 – 1 Then the integrand decomposes into the…

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Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: Use a sixth-degree Taylor polynomial centered at zero to approximate the integral. Function…

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Q: Evaluate the integral dx (2x + 6) by making the appropriate substitution: u = dx (2a + 6)°

A: To evaluate the given integral.

Q: 9-x2 B: Find the integral S 18-x2-y xydzdydx.

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Q: In Exercises 15-34, calculate the integral.

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Q: 7x Evaluate the integral -d.x. (x2 + 1)(2x – 2)

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Q: Evaluate the integral (x – 1)ez xp- x² – 2x + 2

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Q: Consider the definite integral. (10x - )x – 1) ex²-x dx Let u = 5x2 – x. Use the substitution method…

A: As per our company guidelines we are supposed to do only first question. Kindly repost the other in…

Q: Evaluate the integral. dx i. 2 x²Vx2–1°

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Q: 4x4 + 1 dx J 2x3 + x2 – x

A: Given integral is: I=∫4x4+12x3+x2-xdx Integrating it by using partial fraction decomposition:…

Q: – 30 - Evaluate the integral: -d.x x2 Vx2 + 16

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Q: [4] 5. Use the fact that 1 +C 4e2r dx = 2e2 to either evaluate the improper integral 2 dr, or show…

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Q: dx Evaluate the integral: 3/2 64 -

A: To solve the given integral problem.

Q: Evaluate the integral. 9. dx J2 (x² – 1)3/2

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Q: Find the indefinite integral: (t3/2 + t-1/2 - 10t-1) dt

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Q: Evaluate the integral d.x (V4 – x²)³ 0. -

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Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Show that if an integration formula of the type I„(f) =£w;f(x;) j=1 is exact for 1, x, x², ...x",…

A: According to question given:Inf≈∑j=1nwjf(xj)Is exact for 1, x, x2, ...xm for a natural number m.We…