12 1 3. Find the exact value of the definite integral | dx (x+6) Vx- 3

Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: 1 Vx + 10 — о(х), х — 0 te-2n 10n В. о(1/п), п — о 1 — о(е "), п — sin æ = x- +0(x°), x → 0 3 D. n2…

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Q: QUESTION 2 a) Evaluate the following integrals with respect to x. i) f9x cosech (3x)dx -0.5 xsin¯'x…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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: 5 Find the following indefinite integrals. 10 a. f(x+2)' dx b. J d. [4 (3-&x) dx c. (3x-7) xp-

A: c)

Q: 3- Find the Gamma and Beta definite Integral below: 3-1- x1.5 X. dx

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Q: 15-56 Evaluate the integrals √x²√5 +x+dx X 45ở dx sin(1/x) dx 3x²

A: We have to find the value of integration using appropriate substitution.

Q: Q4. (a) Evaluate the definite integrals: (i) ſ(2 – 5/1 – x² }tx_ (ii) [sin 2x cos 2x dx (iv) [":…

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Q: 1. Find the definite integrals of the following functions : (a) L. 4.x dx (h) dx ex +1 -2 0. (b) /…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: TL 2 Evaluate the integral: sin(3x)cos(3x)dx 3 1 A B C D H|m 3 16 1 3 16

A: To evaluate the integral. Option c is correct.

Q: 1 16r 10. Evaluate the definite integral | dr V16-r² 11. Evaluate the definite integral 4 + sin 2x)'…

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Q: 1. Find the antiderivative of each of the following functions. 3 a. f(x) =+ e* + Vx b. f(x) = sin…

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

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

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Q: f(x csc² 2x - x cos x cos 2x)dx

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Q: Evaluate the integral. dx 1

A: givenI=∫13x2dxwe know integral formula∫xndx=xn+1n+1+C

Q: Question 1. Evaluate the following integrals using substitution method: |(x-1)(x²–2x)"dx_ a) sin°…

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Q: 23x+3+42x-1 6. S dx 2x+3 In(sin x) 7. S- tan x | Voty csc' y dy 8. dx 9. x log 10 x e" dr 1 + e" 10.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Question 4 Evaluate the following integrals: (a) / dæ x2 +4 * T/4 (b) etan(x) sec? (x) dæ 0. x3 – x2…

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Q: 1. Evaluate the integral |(x² - 5)e*dx 8.

A: Given that: ∫0∞ x2 -5e-3x dx To find: The value of the given integral. Let I = ∫0∞ (x2 -5)e-3x dx…

Q: 5x+6 Consider the indefinite integral e+0 dx:

A: given equation= e5x+6

Q: x 3*dx Jo

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Q: 1. Evaluate the integral of x2 (3 - 2x) dx if upper limit = 2 and lower limit = -1. а. 12 b. -12 C.…

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Q: Find the solution of the initial-value problem. dx 5 sint x(0) = 4 %3D dt X= (Use integers or…

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Q: 1. Find the most general antiderivative of the function 12 f(x) = ( 2r + sin(4- r) + 7e

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Q: 12.1 12.2: Problem 2 Evaluate the iterated integral: 1 x + 4y dx dy 3 Answer :

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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: POS jma- 3 d 1 sin t dt %3| dx 1 1 (A) – x sin(x²) (B) sin(x²) (C) x sin(x²) (D) –sin(x²) ов O O O O

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Q: Question 5. Evaluate the definite integrals. a) 8x dx .5 b) S 2 dy

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Q: The following integral is  The integral of g(x)dx from 7 to 2

A: The given integrals are,

Q: Question 6. Evaluate the indefinite integral 1 - dx. J x(x² + 2x + 2)

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Q: 7. (4ea) Evaluate the definite integrals. a) L (3x2 + e*) dx

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

Q: Question 5 Evaluate the integral and choose the correct answer. Sx [x²1 01 x² ln x dx 01 1 ³x³ + C 3…

A: Evaluate the integral of the function x2lnx w.r.t. x

Q: 1. Use properties of the definite integral to solve the following problem. f (x)dx = -3 and f(x)dx =…

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Q: 4. Evaluate the integral 3x2 + 13.x + 11 dx I (x+1)(x +2)²

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Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

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Q: 6) x²y" – 3xy' + 5y = 0 ;yı = x² cos(ln x)

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Q: -2 Evaluate the definite integral S: 1 dx. 1 x+a²

A: general answer is Ln|(2+a^2)÷(1+a^2)| Where a = -3/5 Final answer is Ln|59/34|

Q: 1/4 we use the substitution u = (x²+1)² on the definite integral (x³+x)(x²+1)23 dx then the integral…

A: From the given problem: I=∫01x3+xx2+123dx...1 Let, u=x2+12 Now differentiate with respect to x on…

Q: 0 1 Q3:Evaluate the integrals [(x+y+1) dx dy -1-1

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Q: Problem 11 Evaluate the indefinite integral.  ∫sec^3(x)dx=____________ +C

A: Given integral can be written as Integrating by parts, we get

Q: 2 sin x Verify whether the function g(x) =1- is the solution of the integral equation [1 – (7/2)]…

A: The integral equation gx-∫0πcosx+tgtdt=1 is a Fredholm integral equation. We have to check whether…

Q: |(16x3 - 3x2 + 4) dx (16х3

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Q: I'm having trouble figuring out why the integral of e-3x dx is equal to (-1/3)e-3x. I do not know…

A: Given:    f(x) = e-3x

Q: -3 -4 1 3 4 6 7 Compute each of the following definite integrals: (a) / s f(x)d.x. 10 (b) / f(x)dx.…

A: (a) ∫04fxdx This integral is given by the area under the curve. This area can be divided into 3…

Q: [5.7 Problem 402] Find the following indefinite integral using appropriate substitutions. dr 1리V422…

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

Q: (x – 4)e dx satisfying the initial condition y(4) = In(4). ソ= Your answer should be a function of x.

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Q: Question 2: Use the Green's theorem to solve $(v² +3x² \dx+2xdy which bounded by x=0,y=0 and 4(x² +…

A: We find the given integral by using Green's theorem.

Q: 4. Find the explicit particular solution of the initial value problem give dy -уе , у(0) %3D 9 е 8x…

A: We will find the solution to the Differential equation.

Q: 23. (a) (2n )! [P,(x)]² dx 2 (n!)ª J_, (1 – x*y" dx (b) By making an appropriate change of variable,…

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Q: Find the exact value of the integral. Question 1 4 V2 + x'dx dy

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