Evaluate the following integral. dx V(x - 1)(7 – x) Rewrite the radicand by completing the square dx dx V(x- 1)(7- x)

Q: Q1 - Evaluate the following integral: J (2x2-3x+2) dx (x-1)2 (x-2)

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Q: Evaluate the integral. 3 x e* dx = +C

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Q: c) Evaluate the following integral | dx. x2 +6x+10

A: x2+6x+10=x2+6x+9+1x2+6x+10=x2+2*x*3+32+1    (a2+2ab+b2=(a+b)2) x2+6x+10=(x+3)2+1

Q: 6 (x²+1) dx S (23+3x-2)²

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Q: Evaluate the integral. dx a > 0 + x²)3/2? 4 Jo (a2

A: given, 4∫0adxa2+x23/2 , a>0

Q: Evaluate the following integrals: dx dx ·S b. S √81+16x² √16x²-9 a. dx 49-4x² c. S.

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Q: 3 9-x 1 dy dx dz V9-2? (x² + y²)1/2 3

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Q: evaluate the given integral.

A: Use Substitution method to determine the value of  integral .

Q: Express the integral a.e •e²² dx in terms of the integral dx .

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Q: Evaluate the integral. (x2 + 6)e¬X dx

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Q: Evaluate the following integral. dx J secx-1 dx sec x-1 (Use C as the arbitrary constant.)

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Q: dx 4 sın*3x tan

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Q: Evaluate the integral. (x² + 2)e¬× dx

A: To evaluate:∫01x2+2e-xdx

Q: Evaluate the integral. dx 4 a > 0 (a² + x²)3/2?

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Q: Evaluate the definite integral: 4 dx 0 x2+16

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Q: Evaluate the indefinite integral. 1x - 3 dx J (læ2 – 6x + 4)3 Answer = +C

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Q: Evaluate the integral. x2 e dx +C

A: Here, to evaluate: ∫8 x2exdx=8∫x2exdx

Q: Evaluate the integral. 1 (x² + 3)e¯× dx 0.

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Q: Use the indicated substitution to evaluate the integral.

A: Given:           ∫012x21−x2dx,  x=sinθ

Q: Q1: Evaluate the following integrals by using a substitution to reduce it to sec X dx 1 standard…

A: We have to use substitution method.

Q: dx 51. 1 + e*

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Q: Find the indefinite integrals: x5/2 + 4x + 1 dx a) / ? b) / (a" 6t7 2 + Te' ) dt t3

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Q: Evaluate the definite integral.

A: Now consider,

Q: Use any appropriate method to evaluate the following integral: (x^3)*(e^(x^2)) dx

A: Simple Integration problem....

Q: Find the following indefinite integral. I dx x2 + 9

A: From the given problem:   I=∫xdxx2+9...(1)   Let,   x2+9=t   To differentiate with respect to x.…

Q: . Evaluate the integral, if it exists. L(** – 3x/3 + 1) dx а. i (20* -) dx b. 2e* X.

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Q: Q1 - Evaluate the following integrals i. " xe-*dx

A: We are evaluating the following integral:

Q: The integral 1 dx x2 - 4 x + 4 ? If the integral is a number, enter the value in the blank below. If…

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Q: Find the following integral, given that f (x) dx = 10 and | 6)*dx = 14. 9. b.

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Q: Evaluate the integral or show that it diverges e dx 1+e-x

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Q: use the indicated substitution to evaluate the integral.

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Q: Evaluate the following integral or state that they diverge.

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Q: Evaluate the following integral. -0.8x dx 3 e S. -0.8x dx = 3 e (Use C as the arbitrary constant.)

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Q: Evaluate the integral. 4 – e2× dx = +C

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Q: Evaluate the following indefinite integral: dx r2 +1

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Q: Evaluate the integral: x² e3a dx

A: This question is related to Indefinite Integral, we will use Integration by parts formula to solve…

Q: To evaluate the integral * dx we use the substitution e а. x2 1 O b. 1- x2 O d. x + 1 =t

A: Explanation of the solution is given below...

Q: Evaluate the following integrals. (а) 1 (&r + 1)572 dx (b) -dx Vx

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Q: (b) Evaluate the integral | xe * dx. (1- x)?

A: Given : The integral is ∫ xe-x (1-x)2 dx .

Q: dx 3 Vx Vx (1+Vx)²

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Q: Evaluate the following integral. x2 dx V1- 144x x2 dx = V1-144x? (Type an exact answer. Use…

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Q: Evaluate the given integral. 1 a) dx ² +x – 2 3 b) dr 3 – 9x2

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Q: Evaluate the integral. 5 x2 e dx +C

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Q: Determine the following indefinite integral. dx |( + x7) dx= O

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Q: Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

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Q: Evaluate the integral. (Use C for the constant of integration.) x³ + 9x² + 2x + 9 dx T Tx? + 1)(x² +…

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Q: A. Evaluate the following integrals 1. 2. L. 3. , e*dx dx dx -1 x2/3 4. SE tanodo -4 dx

A: solution:-Q.(4) ∫-∞π2tanθdθsolving the improper…

Q: Evaluate the following integral 1 dx (x – 5)²(x + 3) a

A: We have to evaluate the given integral    The given integral is   ∫1(x-5)2(x+3)dx

Q: Evaluate the integral. 2 e 1/x5 dx

A: Rewrite the function as follows: ∫12ex-5x6dx