) L -dx (x² + 1)²(x² + 2x + 2)` sen? t dt, for 0

Q: dx 1 converges or diverges, it would be useful to compare the integrand to To determine if a2 + Va…

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Q: Evaluate the integral dx 2x x - 3x? 1 V3 + V2 x u- - V7 VX + C 2/3 TV3 1 In 2/3"/7x + V3 +C -In 4…

A:

Q: Compute or show divergence: 1 а. dx 3 Vx+1

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

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Q: 1 Prove that the integral : Tz dx is convergent. 1+x

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Q: 6. The improper integral dx converges to /x- 5 '5 Vr-5

A: The given integral is an improper integral of second kind.

Q: Evaluate the integral. /x² – 36 Vx2 – 36 -dx + 6cos + C Vx² – 36 -dx = Vx² – 36 – 6cos- () + C x² –…

A:

Q: Conclude on the convergence or divergence of sin x dx cos x

A: Since function is not continous at x=pi/2. Hence we break the limit of integral at x=pi/2. This…

Q: find integral x3 3) S dx /1-x²

A: We have to find the indefinite integral

Q: 2メーx2 Compute the integration dydx (x²,

A: Given:          ∫12∫02x-x21x2+y22dydx       Converting into polar coordinate  It looks like half a…

Q: 13 1 dx V13 - O convergent O divergent

A: 13-x=z-dx=dz∫113-x3dx we need to find.

Q: 4. Indicate if each improper integral converges or diverges. a) ['te*dt dx c) Lo1+x -2t а) b) x -1…

A: The given integrals are: a) te-2t limit from 0 to infinity.  b) x/(x2-1) limit from 3 to infinity.…

Q: 1. Evaluate the integral 5x + 1 dx 2x2 - x -1

A: We can evaluate the given integral by using the partial fraction method.

Q: 27. tan'x sec x dx 30. tan r dt

A: the basic formulae must to solve these problems: 1) ∫xn dx =xn+1n+1+c2)d tan(x)dx= sec2(x) 3) d…

Q: Determine whether the improper integral diverges or converges. dx 1. (2x-1)3 7 dx 2. -1* + 1

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Q: 5 2 +2 ) dx using Estimate I - n = 4 subintervals and (a) Left endpoints. (b) Right endnoints.

A: solution:-I=∫152x+2dx,     n=4f(x)=2x+2∆x=5-14=1(a) Left end pointI=∆xf(1)+f(2)+f(3)+f(4)…

Q: 5 3 ) f(x) = 4x+ x°+7x-2 Show that 4x$+ x²+7x-2 =0 has only one real rot.(Hint App!ly INT and MUT to…

A: Given,  f(x) = 4x5+x³+7x-2   This is algebraic equation, which is continuous and differentiable in…

Q: dx 3) L. Vx+1

A: Given:

Q: 12. Suppose that g is integrable and that g(x)dx = -7 and [8(x)dx = 2. d: g(x)dx

A:

Q: 3. Does the improper integral 2 dx converge? et +e-*

A:

Q: 10. Determine whether the improper integral converges or diverges 3 dx (x – 1)3 -

A: Given query is to integral converges or diverges.

Q: 30. Determine if the integral dx is convergent or divergent c. Neither a. Convergent b. Divergent d.…

A:

Q: Perform a test to determine if it converge or diverge -1 x 2sin 1 dx 1– x -1

A: The function is given by: ∫-112sin-1x1-xdx If the function fx=2sin-1x1-x is positive, continuous and…

Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral:…

A: This question is based on chain rule differentiation and indefinite integral.

Q: (4)Evaluate the definite integral (a)S(1 + sin x )£x 1/2 (b) [ (2t + cost)dt -*/2 x +1

A: As per the Guidelines, I will answer the first 3 Integrals. For the fourth one please repost the…

Q: 8 Evaluate the integral dx using the two-point Gaussian quadrature rule. 16+z1 -2

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Q: Example 11: 3 If F(x) = J Int dt, find F'(xr) 2+sin 2.x

A: To determine the F'(x).

Q: 3 Evaluate the integral |x V2x +1 dx ?

A: ∫x22x3+1dx We need to integrate the given function.

Q: a) [ Evaluate the integral 4x - 1 (x + 2)(2x - 1) S -dx.

A:

Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: 7. Use integration by parts to prove that for any positive integer n, | cos"x dx = 1 cosn-1xx+ n - 1…

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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…

A:

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: of P converges Find the Value which the integral absoluley condition. Sin () dx

A: To find the value of p for which the integral ∫1∞sin(1x)xpdx  converges absolutely. The improper…

Q: O f(3x² + sec² 2x) dx

A: Given query is to find integral.

Q: An odd piecewise continuous function f(x) on every finite interval of (-0, 0) such that / fx)| dxis…

A:

Q: Compute x² In a dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's 3/8…

A: For the solution follow the next steps.

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: (2x+5)² 2. What should be the rewrite of the integrand of ſ x2 dx so that the resulting integral is…

A:

Q: 2. Evaluate the integral: 2xe-**dx -0

A: topic - integration

Q: 4.) Evaleuate the integrali Jóxarcsin(5a)dx

A: ∫fg'=fg-∫f'gAnd ∫sinnxdx=n-1n∫sinn-2xdx-cosxsinn-1xnsee below the answer and calculation

Q: An even piecewise continuous function f(x) on every finite interval of (-oo, 0) such that :/ (x)|…

A: The given statement is : An even piecewise continuous function f(x) on every finite interval of -∞,∞…

Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

A:

Q: Evaluate if the integral converges 1. 1. dx (x-1)7 , sin x dx 3. dx 2.

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Q: 7. Evaluate the integral. Vx2 – 25 dx х3

A: First we will make a trigonometric substitution of x=5*sec θ then we will solve it and integrate it.…

Q: Compute the definite integral 2 dx Vx² + 4

A: First, we need to compute ∫xx2+4dx

Q: Find the partial integral. (3х + 5y) dx

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Q: 5. prove that d (-x) (+ x) = X dx dx d² dx² - x² +1

A:

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: Evaluate the double integral : 9 dy dx 36 – 12 - 12 -36

A: