1. Determine whether the following pairs of operators commute dx х (a) (b) dx

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A: Given that expression we have to find evaluate the value

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Q: dx Vx + a + Vx + b

A: Given: The integral is ∫xx+a+x+bdx

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Q: -1) dx 3

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Q: dx. = 9) Evaluate 2x-1

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Q: e-(6x+5y) dxdy

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Q: .2 dx Jo (9 + x²)2

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Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: -1 -x d. Let A = 2 2 1 2 i. |A| =

A: Given that: A=-x-1-xx2x212

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A: Given : ∫233x2+2x+1x2dx

Q: Show that: -1 xb-1 In x dx b2 2-

A: we use integration by parts

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Q: 1 3. Evaluate dx, using substitution method. 2

A: The given integral is: ∫1xx+12dx I=∫1xx+12dx    -1

Q: Evaluate x(x2 + 1)3 dx.

A: Given ∫x(x2+1)3dx

Q: dx. x2 V1+ x2 Evaluate

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Q: 1. Find dx. x2 + 64

A: I = ∫1x2x2 + 64 dxLet x = 8 tanθ     dx = 8 sec2 θ dθx2 + 64 = 64 tan2θ + 64                 = 64…

Q: If 7-4/3 = Vx-Vy, determine the values of x and y. %3D

A: We have to find the values of x and y from the above expression.

Q: dx Evaluate -1 x2 - 0 -2

A: The integration formula is ∫xndx=xn+1n+1+C.

Q: Evaluate f x²n. x2n-1 x + 1 dx.

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Q: Evaluate х2 + 2х — 1 х3 — х

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Q: 2. Find b such that dx 1+x2 3

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Q: w = (1³ + 11)8| dw dt

A: Given :   To find