Obtain the value of P3 (x) using Rodrigues' formula d" P,(x) = (x² – 1)" (2")n! dx"

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Q: Find ∫√(2x − 1) dx.

A: Given:

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Q: 3.2 (2x - y²) dxdy

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Q: (c) Use geometry (ONLY) to find the exact value of (2x + 1) dx. Illustrate your method with a new…

A: By sketching graph

Q: (2x³-9x²+2) dx from x = 6 to x = 11

A: Given: ∫2x3-9x2+2dx   from x=6 to x=11

Q: 2 [+√²-1)dx (4) »

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Q: Find ∫ dx/√(e2x − 1)

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Q: As a → 1 what happens to the value of f f(x)dx?

A: As a →1 what happens to the value of ∫1af(x)dx.

Q: .2 dx Jo (9 + x²)2

A:

Q: Solve for k such that 1 | k(x² – 2x + 1)dx = 5

A: Given problem:- ∫ k(x2 -2x+1) dx =5  Solve for k

Q: 1. [(2x-3) (4x2– 12x)* dx

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Q: Find if y = (x² – 1) (x³ + 2). dx

A: We expand the given expression and then use power rule to find the derivative.

Q: Use the keyhole contour to show that dx а. V3 2n? xl/3(x + 1) logr b. -dx c1/3(x + 1) 3

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

Q: 3. Solve the following: 2xdx (x²+1)2 a. b. y = f xe* dx, given y=0 when x=0 x-2x+1 dx с. d. sn (Inx)…

A: According to our guidelines we can answer only first three sub-parts and rest can be reposted.

Q: 1. [²+3x - 4)dx

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Q: B) Solve the following 3x -dx (x + 5)(2x - 1)

A: Topic = Integration

Q: Find p, q if f,º f(x) dx – L f(x)dx = [" 5(x) dx. (Give your answers as whole or exact numbers.) p =

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Q: 9 4 2 10x²¹² + 3 dx √x

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Q: 1/(x³ – 8) dx

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Q: | (b) b)5zVE+z-/2 dx.

A: To evaluate the given integral

Q: iv) L,x²e=* dx -2 -3x dx 1

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Q: (き4-)

A: This integral can be solved by the substitution method.

Q: 21 (b), dx -1 3e2x

A: