S (-1,3] U [5, 6) Ø {x ln(x) x>0} inf (S) sup(S)

Q: T² 2 / (x + 1) (2² + 1) dr. Evaluate

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Q: 9. 3 If f is continuous and f (u) du = 3, then / (4xf(x²) + f(3x)) dx is equal to

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Q: f(x) = ln[x(x + 6) 5 (x²+2)4] f'(x) =

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Q: t' sin(2t n(21*)dt Evaluate

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Q: Let plx)= 6x f(x) f"(x)= f"(-2) = 5-3 %3D 2.

A: Recall: dxndx=nxn-1

Q: IfY C X, show that inf (X) < inf (Y)

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Q: If f, g L₂ then [S* S(x)g (x) dx ] * ≤ [f*° ƒ^²(x)dx ] [1° g² (x) dx]

A: This is the famous Cauchy Schwarz inequality for integrals. It follows by working with quadratic…

Q: Evaluate csch- x dx , 0 < x < 1

A: To find the integration of following csch-1x

Q: Compute f(x)dx 2x if x 1 f(x)

A: To find out the integration.

Q: find the fallowing Js(x)

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Q: Evaluate the function when x = 1, 3 and 3 3 1) f(x) = x + 2x - 3

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Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

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Q: L' -2s Find f s2

A: Inverse Laplace transform

Q: 10 6. Evaluate -dx. (x – 1)(x² + 9)*

A: Given integral is We will evaluate the integral by using the concept of partial fraction…

Q: Find f. f "(x) x2, x > 0, f(1) 0, f(9) 0 =

A: Given,

Q: y=ー-x+5 3 y=-x+7

A: This question is based on Substitution.

Q: S dx b² +x4 - Evaluate

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Q: f(x) 1 2 2 1 3 3 4 -1 f'(x) g(x) 3 4 -3 -2 -1 1-2 3 12 |-4 -1 0 -3 g'(x)

A: According to latest Bartleby guidelines, we can answer only first three subparts, please post other…

Q: or f(x) = 2x-7 3x - 2

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Q: . Evaluate S (-+ 3e* ) dx

A: We have to Evaluate  ∫ {(1/√x) - (2/x) + 3ex} dx = ∫(1/√x) dx - 2 ∫(1/x) dx + 3 ∫ex dx

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: dr(sec'x) dx

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Q: 2 [*x* (Inx)² dx

A: Given integration is evaluated.

Q: S x(1 + x³)"'dx

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Q: Show E(XY)

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Q: d/dx[(1-cosh(x))/(1+cosh(x))]

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Q: cosh(In x) dx

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Q: Integral 1. xp x²(x - 1)

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Q: X -₂(x - 2)(x + 3) -2 dx

A: given