Exercise 1.2: Apply integration by parts a second time to get 272 2(1-2²) 2n x 2n 2(1-2²)-¹ sin(x2)dz = 2m ₁ [(1 – 2²)n-¹ – 22²(n − 1)(1 -- 2²)n-²] cos(xz)dz

Q: 7/4 2 sec(6x)dx sin(r In(x)) 13x 1

A: (b)

Q: If f (x, y) = x(x² + y²)-3/2 esin(a²y) find fa(1,0).

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Q: Use a three-point numerical integration rule to approximate the following: 1 e* (x+4) 0 dx

A: As per the question we are given an improper integral which we have to numerically compute using a…

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: Simplify (if necessary) then 2 Compute: y" +Éy' for a2 y(z) = rar (zx+ cosx')] [6(cosh2x- sinh2x)] d…

A: given yz=∂2∂x∂zz2x+cosx96cosh2x-6sinh2x36cos2πxddx3x2 claim- if necessary simplify then compute the…

Q: Give an expression for p (x) so the integral p(x) cos(7x) dx can be evaluated using integration by…

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Q: (1) Integrate the following functions: (a) I = [ (4x³ − 6x² + 2x²³¹′)dx (²-3)dx 2 (b) I = .3 (c) I =…

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Q: Find f. f(x) = f"(x) = x3 + sinh(x), f(0) = 1, f(2) = 2.6 ×

A:

Q: (a) Using integration by parts, find fx sin(2x - 1) dx. (b) Use substitution method to find x² 2x-1…

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Q: Use the method of undetermined co – efficient to solve: y'' + 2y = sin (x)

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Q: Show that J−1/2(x) = √2/πx co

A: Bessel functions are a family of mathematical functions that arise in many areas of physics and…

Q: For matrix A = (4 6 3 5 ). If f(x) = x2 - 5, calculate f(A)?

A: The given matrix is, A=4635. The function is f(x)=x2-5. For matrix multiplication: The number of…