Use MUPAD to determine the following indefinite integrals (7.1) (7.2) (2ax-x²)³ dx. S (7.3) Obtain a numerical estimate for the following definite integral Canxi dx. sin x ✓1 + sinx dx

Q: Use the Product Rule to find the derivative == [( ²³ ²³² + ² × ³ ) ( ² − 4׳²)] · dx X Answer

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Q: g. y = u² + u³, u = ³ - 4v, v = 3 - x², x = 2 u5

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Q: d cosh(3x? + 1) and (b) dx d (sinh x tanh x). dx Calculate (a)

A: Given: a ddxcosh3x2+1b ddxsinhx tanhx

Q: Evaluate [sin² (7x)dx using Simpson's method to four decimal places. take n = 6.

A: ∫01sin2πxdx       To find: Above integral using Simpson's method if n=6.

Q: Find dy/dx. Do not simplify the answer. 4* +4 csc a.) y = log4 x-csc(4) b.) x3 y + cosh¬1 3 = e –…

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Q: Find the derivative of y = In (tanh x).

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Q: A. Evaluate. 1 (sinhx - sinhx +coshx cosh?x 1. dx

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Q: the ratio d/dx 8csc(x)/csc(x)cot(x) is a constant number. Its value is

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Q: Evaluate. (a) ∫x(x+ 1)^2 dx. (b)∫(upper) π/4 (lower) 0 (1 + 2 secθtanθ)dθ

A: Part a,Given,            ∫xx+12dx

Q: b. sin? () = 2 over [0, 2n) %3D

A: EXPLANATION

Q: Let g(x)=4x csc x. Find the (exact) value of g"(5pi/6)

A: Given:      gx=4xcscx

Q: 1. csc² x cot rV csc x –1 dx

A: