Use the Beta and gamma function -1 n! 1- Prove that x™(ln x)"dx (m+1)n+1

Q: Determine if the improper integral converges or diverges: 1 dx. 1+x²

A: Our Aim is to determine whether the improper integral given below converges or diverges∫0∞11+x2 -(i)

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

A: No.2 The improper integral is of second kind where f(x) = 1/(x+1) has one point of infinte…

Q: 3. Use the Comparison Test to determine whether the integral cos? x dx is convergent or divergent.…

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Q: a=1 and n-1. Let f(t) = tet SHOW all of your steps of integration clearly.

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Q: Solve the integral. 1+ In x 8. -dx J x +x In² x

A: The given integral is  I=∫1+ln(x)x+x ln2xdx The integral can be calculated by doing substitutions.

Q: 73. Use the definition of |x\, the chain rule, and the fact that (In x) = - for x > 0 to prove that…

A: Given, dlnxdx=1x, x>0 from definition of x x=x ,     x>0 -x ,  x<0  if x>0 then d…

Q: Find out if the improper integral converges or diverges. If the given converges, find its value.…

A: Solution

Q: d Prove In Jax| dx In x for any constant a. dx

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Q: Determine | An (x) An+1(x) dx, from the relation: tn .1 Σ (2n + 1)! tn+1 A, (x) An+1(x) dx n=0 n -1

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Q: Derive a formula for In x dx where a. nt-1 b. n=-1

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Q: 1. Evaluate the ff. integral f, (5x6 + 3x³ + 6)dx ·1

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Q: Evaluate the integral. HINT: 3 x2 dx J2 x - 1

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Q: Consider the following.   x4 + 3)2(4x dx)      Use algebra to rewrite the integrand by expanding the…

A: Given (x4 + 3)2 (4x dx)

Q: Use mathematical induction to prove that the n-th derivative of (x +n + 1)e" is given by d" (x+1)e =…

A: We use mathematical induction. The detailed solution is typesetted and given in detailed as the next…

Q: 5. Find the integral 1 -dx x -5x +6

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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: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

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Q: Evaluate the integral if it converges. Enter the exact answer, or enter na if it diverges. +00 -dx =…

A: Let I is the value of given Integral.

Q: (a) Evaluate the integral 1 2 (4-)dy dx

A: Evaluate the given integral as follows. ∫01∫024-y2 dy dx=∫01∫024-y2 dy dx=∫014y-y3302 dx=∫018-83…

Q: Use integration by parts to prove the reduction formula: п-1 S (In x)"dx = x(ln x)" – n [ (Inx)"-! п

A: 2

Q: Prove that coshz =log ztv= {Hint : cosh z =e} 2.

A: Use the hint and prove this.

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. .......Integrate f over the given interval of x, using…

A: Solution:

Q: -dx converges or diverges. Justify your claim. determine if the integral 1+ cos? r

A: Introduction: When the integrand becomes discontinuous at any of the limits of the given…

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: Find the linear approximation of f (x) = ln e at L() In(1.42) 1 and use it to estimate ln(1.42)…

A: Given function is f(x) = ln x and the linear approximation is to be calculated at x = 1.Linear…

Q: At the point of discontinuity on(0, 00), the Fourier Sine integral converges to: OA None f(x+) -…

A: Here  At the point of discontinuity on  0,∞ the Fourier sine integral converges to

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: Consider the integration of f(x) = 1 + e* sin(4x) over the fixed interval [0, 1]. Apply composite…

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Q: d) Numerically approximate the integral 2+ cos(2Vx) dx by 3 Simpson's rule with 6 strips

A: Given integral is ∫022+cos2xdx. To evaluate the integral using Simpson's 38 rule. Consider the…

Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x*-1sin x…

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Q: Compute dx using the techniques as presented in class and in our textbook. Show all 2x +5x-3 the…

A: we first factor the denominator

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: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

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Q: Find the Fourier integral of the function f(x)= e* when x> 0 and f(-x) = f(x) for k > 0 cosix and…

A: Fourier integral, for even function

Q: Show that integral 0 to infinity  x2 e -x2  dx = 1/2 integral 0 to infinity e -x2  dx

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Q: Find the integration of (1+ 2x)dx using Trapezoidal and Simpson's Rules for n=6

A: Given integral  ∫061+2xdx The Trapezoidal rule states that…

Q: Determine whether the integral is convergent or divergent. *e-1/x dx x2

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Q: 5. Express the integral: e- dr in terms of gamma function.

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Q: or show that the integral Integrate the following diverges: Зе In sin x ii) dx COS X 2e

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Q: 27 e integral dx be transformed into one of

A: By using a trigonometric substitution x=3secθ where, 0≤θ≤π2. The integral ∫27x3x2-9dx can be…

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

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

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Q: RA Find dx dt x In(x) /1 + (In(x))²

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Q: Q5. Approximate the integral Sin(2x)dx (i) Using composite Sympson's rule with n = 2,4 and

A: As per the policy of bartleby the provisions is to solve only one question at a time so I am solving…

Q: Using Simpson's (1/3) rule with h = 1, evaluate the integral: 7 = f x² logx dx 3

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Q: Use the Romberg integration to evaluate. 3 xe*dr With an exactitude e =0.5%

A: Given ∫03xexdx whose step error should be εs=0.5%. We use the Trapezoidal rule…

Q: Use the second fundamental theorem of calculus along with the chain rule to find d sint dt dx 1 o…

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Q: Evaluate Poisson Integral: In(1-2a cos(x) + a²) dx ,a.) [a| 1,

A: To evaluate Poisson's integral: ∫0πln1-2αcos(x)+α2dx  a)α<1 b)α>1

Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

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

Q: Use U-Substitution to evaluate the definite integrals. Sž cos 2x dx (1+x2)2

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