The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y 12 y = g(x) X 12 21 (a) хр (x) * 18 g(x) dx (b) *21 (c) g(x) dx

Q: is The antiderivative of the function f(x) =. 2x а. 2 In x + c b. 1

A: Givenf(x)=12xAntiderivative of f(x)=?Antiderivative is nothing but integral.

Q: Q9/ find the integration ſe^( (2x) ^3-1) x2 dx? * 1 а- 6. e2x* -1+c 1 b- e2x3 +C 1 .2x3–1+

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Q: dx b. (x² + 1)(x² – 2x + 1) -

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Q: Find the antiderivative of xe2x/(1+2x)2 from 0 to 1/2

A: Given the integral ∫012xe2x1+2x2dx

Q: -x + 2 dx . x2 + 2x ate the integral

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Q: Consider the function f(x) = 16x³ - 21x2 + 6x – 8. Find F(x) an antiderivative of f(x). F(x) =]

A: Topic - integration

Q: dx Evaluate the integral V1 + 9x² 1)

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Q: If g(1) = -1, g(5) = 2, and | g(x) dx = -9, evaluate the integral %3D æg'(x) dx.

A: Given: g1=-1  and g(5)=2∫15g(x)=-9

Q: Evaluate the integral. V3/2 19x2 dx V1 - x2

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Q: 2 3x 2. Evaluate f x'e* using integration by parts.

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Q: find the absolute extrema of thefunction on the closed interval. y=x^{2}-8 \ln x,[1,5]

A: Given:- function y=x2-8 Inxdefined on the interval 1, 5 The derivative of the function is y'=2x-8x…

Q: dx. Evaluate the integral / (x² + 1)(^ · x – 2) -

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Q: a. Find the antiderivative of f(x) = -25x e F(x) = %3D

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Q: dx 1. S (x²+1)(x²-4)²

A: Use partial fraction to solve it.

Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: Evaluate the integral. | (e7* +3e -x) dx 7X +3 e -X) dx=

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: Find a ≤ b such that

A: ∫abx2-9dxApply the Sum Rule:…

Q: dy + ydx %3D 3x²y?dx,

A: Given differential equation is bernaulli's differential equation.,  and we can solve it by reducing…

Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

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Q: te the Integral. 1 xV1- x2 dx 14

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Q: Find the integral. |(2x3 - 3x2 + x – 1) dx A x² + B 6x2 - 6x + 1 + C (c) None of the above x2 - x +…

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Q: Evaluate the integral. 9 17 1+ x2 dx V1- x2 +C

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Q: 11. Find two different antiderivatives of the function f(x) = 6x² +2ex. 1

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Q: 9-x2 18-x²-y² xydzdydx. B: Find the integral fo J

A: Triple integral

Q: -dx. Q5. Evaluate the integral / Tx² + 1)(X · x – 2)

A: Given  α=5 ,β=8 ,γ=13,λ=2 ,θ=5 , η=3 ,ω=2 . To rewrite the given integration by using α=5 and λ=2 .…

Q: A b B d a The integral 15x²x³43x - 19 (x + 1)²(x² - 6x +13) can be rewritten as Ax + B D C + ax² +…

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Q: Evaluate the integral x3 dx 2+100 S x3 dx +100 (Use C as the arbitrary constant.)

A: Given,

Q: 7x Evaluate the definite integral : dx (6x2+2)2

A: Given,          ∫017x6x2+252dx

Q: Find the most general antiderivative of f(x)=−7x^2+8x−2. Note: Any arbitrary constants used must be…

A: An anti derivative of a function f is a differentiable function, whose derivative should be equal to…

Q: Find the most general antiderivative of the function. 2xA + 7x³ - x F(x) + x >0 %3D F(x) %3D

A: Given that     f(x) = (2x4+7x3-x)/x3 We have to find the antiderivative of the function.

Q: Find the general form of the antiderivative of g(x) = - cos4x

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Q: Find the most general antiderivative of f(x) 2x-1+x.

A: Given,            f(x) = 2x2 - 1 + x-2

Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

Q: (2 |2* 2 –1 – 1|x dx

A: Topic:- Definite Integration

Q: You are told that Lif(x) dx = 9 and /, 8(x ) dx = -2. what is the %3D value of the definite integral…

A: To Determine: what is the value of the definite integral∫-173fx-4gxdx Given: we have ∫-17fxdx=9 and…

Q: Q18: Evaluate the definite integral: 4x dx V1 + 2x²

A: To find the definite Integral  Substitute 1+2x^2 = t and change the limit accordingly

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

A: We have to calculate the given intregration

Q: 21.3 xdx V16 - 9х4 0.

A: We to integrate the given integration.

Q: 3. Find the integral. 2x dx x2 + 10x + 29 а.

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

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Q: dx S x2 ( 4. x²+x+1)

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Q: Q.4 Using the method of substitution the integral fxer-3 dx

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Q: (7Vx2 7V22-9 6. Evaluate the integral: dx x4

A: Given that I=∫7x2-9x4 We can use the substitution technique.

Q: Evaluate using integration by parts o D (x²-3) e² dx е

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

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Q: Find the integral [(x** +(-1)°x*!) In((a+2)x)dx b+1 с+1

A: The integral has been solved n attached in the second step.

Q: f(x) = Vx2 + xVx %3D

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Q: 1. Use algebraic manipulation and (if necessary) u-substitu- tion to integrate the function. (a) /…

A: Hey, since there are multiple questions posted, we will answer the first three subparts of the…

Q: Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

A: