Evaluate the integral. 4 dx (x – 4) (x – 1) | (Use symbolic notation and fractions where needed. Use C for the arbitrary constant.) 4 dx = (x – 4)2(x – 1)

Q: 12. What value of b> - 1 maximizes the integral? b A nolh | x-(1-x)dx Simplify-1 following…

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Q: Q.1 Find the integral of f 2 /x+ e* ) dx. - 3

A: We will find the integral as following.

Q: dx 6. Evaluate the improper integral. x² +3x+ 2

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Q: 1 So x2-4 dx an improper integral. (5 points each) 3. Find a value of b >0 that makes

A: Given the function :

Q: 12x + 18 1. What is the indefinite integral of / :) dx ? x3 + 5x2 + 2x –8

A: 1)

Q: 4. Evaluate the given integral. |(x + 1)(x – 3)| dx -2

A: Solution:Given∫-20(x+1)(x-3)dx =∫-20(x2-2x-3)dx= ∫-20(x2-2x-3)dx= x33-2x22-3x0-2=0--83-4+6=23

Q: 1. Evaluate the following integral: (1-e-²x) dx (a) analytically;

A: Note:- For this problem all the sub-parts  are different as methods are different. So, we can solve…

Q: Find the indefinite integral.

A: Let ex+e-x=v. Differentiate both sides: (ex-e-x)dx=dv Substitute v and dv in the integral…

Q: x² = 10) Evaluate the integral S dx, x > 3

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Q: B. Evaluate the following integrals: x-9 1) S- dx x2+3x-10

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Q: Q1 Find a particular integral. (D² +5D+6) y= e²* (see'x)(1+2 tan x) -2x

A: Given equation,  (D2+5D+6)y = e-2x(sec2x) ( 1+ 2tanx ) Let us solve the equation for y. y…

Q: Q: 1. (a) Use an appropriate technique to evaluate the integral dx (2x + 1)v4x2 + 4x (b) Evaluate…

A: 1a): Given integral is: I=∫dx(2x+1)4x2+4x=12∫dx(2x+1)x2+xLet…

Q: (a) Evaluate the integral 9x"e¬X dx for n = 0, 1, 2, and 3. n = 0 9. o((-") - (-1)) n = 1 е | n = 2…

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Q: II. Evaluate the following integrals 2x 2. S -dx 2 5+2x+x 2

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Q: Q2) Evaluate the integral x dx a -0.

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Q: (7x-5) The following improper integral (**-x+1) dx

A: ∫1∞7x-5(x+3)(x2-x+1)dx

Q: -1 2x Evaluate the integral dx = 0 x*+1

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Q: 2e Consider the indefinite integral dx: (e2z + 3)* This can be transformed into a basic integral by…

A: Given,

Q: Evaluate the integral. dx (х — 9)(х — 18) (Use symbolic notation and fractions where needed. Use C…

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Q: 0 3. Evaluate the definite integrals: (a) CS Scanned with CamScanner² (x² – 3x) dx (b) 5 1 √I -d.x

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Q: 3. Evaluate the definite integral. Give exact answers S(x² + 2x – 4)dx - a. ~2 2x+1 dx Vx2+x-2 b.

A: Take integration. Follow step 2nd .

Q: 8. Find the value of the constant C for which the integral 11x 11C dx x* + 1 4x + 1 converges. C =…

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Q: 2. Evaluate the indefinite integrals. (a) fx² - 2e*dx (b) Evaluate (3-4x)¹5 dx

A: We have to evaluate the indefinite integral

Q: 3 2 Evaluate the integral| (4- y?) dy dx. 0 0 The value is (Type a simplified fraction.)

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Q: e2x Evaluate the integral: dx 1 + eX

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Q: Зx2 — 4х — 9 A + х — 2 Evaluate the integral J x³ – 2x² – 9x + 18 dx using + х — 3 x + 3

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Q: -5e 1 Evaluate the integral: dx. 1 x A. - - 1 5e B. 1+ In 5 C. 0 D.00

A: We have to evaluate to integrate

Q: 12. Evaluate the integral. x² – 4 – dx

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Q: 8x dx Evaluate the given integral: S; 4x2-5

A: Here we have to evaluate I=∫8x4x2-5dx

Q: Evaluate the integral. S(e* +8e -*) dx | (e 4x +8 e -x) dx =[(Use C as the arbitrary constant.)

A: Consider the given integral.

Q: 8 x2 + 16 dx x2 The integral is equal to ...

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Q: n/4 3x Approximate the integral e "sin(2x)dx using both Simpson's rules with n = п/12

A: Given: I=∫0π4e3xsin2xdxn=π12

Q: a) [ ]: Evaluate the integral (4x + 1) In x dx c) [ ]: Evaluate the integral 2 dx (x – 1)(x + 4) |

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Q: e 2x Evaluate the integral of e* +1 xp-

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Q: x3  (x2 + 9)^(1/2) dx What is the integral of this?

A: Given integral can be expressed as

Q: -3 evaluate the integral (x2 – x + 2) dx using its definition.

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Q: Evaluate the integral. dx (х — 4)(х — 8) (Use symbolic notation and fractions where needed. Use C…

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Q: (ii) Find the following indefinite integrals: 1 (a) dx (b) dx 5 - x* xe* ! dx (c)

A: A)I=∫ 1x3+1x3 dxI=∫ x-3 dx + ∫ x-13 dxI=x-3+1-3+1 +x-13+1-13+1 +CI=-12x2+3 x232 +CI=32x23 -12x2+C

Q: x3+10 x3-2x²+5x f are integers. What is the value of b? X-e The resulting integral of J dx is ax + b…

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Q: -1 х2 Using substitution method, evaluate the integral Jo dx 0 x3+1

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Q: 2 58 n lim dx !! (n+1)? j=1 and the value of the integral is

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Q: 1 (a) for e³x+4 dx Evaluate the following integrals using an appropriate method: (b) √ (3a² +…

A: Given,∫01e3x+4dxLetI=∫01e3x+4dxPut 3x+4=uDifferentiate3dx=dudx=du3As x→0 then u→4As x→1 then…

Q: 13. Evaluate the integral dx x – 1

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Q: Sõlve the integral - In 3 x'e-*dx 2.

A: The given integral ∫0ln3x2e-xdx can be evaluated as, ∫x2e-xdx=x2×∫e-xdx-∫ddxx2×∫e-xdxdx+C…

Q: 5x |(x²+ a) The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers. What…

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Q: 4. Suppose f(x)dx = 6, f(x)dx =5, and g(x)dx=8. Evaluate the following integrals. 4g(x)dx = (32…

A: We make two separate integrals from the given integral.

Q: 7 Suppose f(x)dx = - 3, f(x)dx = - 6, and g(x)dx = 3. Evaluate the following integrals. 2 2 2 g(x)dx…

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Q: Find the value of the constant C for which the integral 5x 5C dx 2 X² + 1 Зх + 1 converges. C = 3…

A: Convergence of integral

Q: Evaluate the integral. dx (x – 10)(x – 15) Use symbolic notation and fractions where needed. Use C…

A: Here we have to evaluate I=∫dxx-10x-15

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…