Let f(t) = 00 n=1 2 6n³ + 3n¹3 -cos(nt).

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Q: x2 Vcos(t) +3 at 1. COS 2.

A: Given that, the integral ∫2x2cos t + 3 dt

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Q: (4) Evaluate cos (2x) -dx. (x² + 1)² 8.

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Q: 7. Prove that d dx [cos ¹ x] = = 1 √1-x² x2

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Q: solve for y, In - y| +C = (1n|cos(x) – 1| +c)

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Q: cos 0 = √√2 -|~

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Q: (xy cos.xy +sin xy)dx +(x² cos.xy +e' )dy=0.

A: We have to solve given problem:

Q: Solve 8(t – nt)cos(-) dt

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Q: Let •T/24 I = tan°(4x) sec(4) dx. Express the value of • T/24 tan"(4x) sec(4x) dx 10 in terms of I.…

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Q: d -(cos(x² – 2x)) dx Evaluate

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Q: 3. dy 1 (y - x°y!)dx = 0 x²y ') dx = 0 %3D dv

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Q: The period of the function f(x) = 2sin3 (x-;) is (b) (c) 2n Q 27 (d); 2 3

A: Here we find the period of given function.

Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

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Q: Prove that d/dx [cos x] = −sin x.

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Q: Use the identity cos alpha cos beta = 1/2[cos(a-b)+cos(a+b)] to rewrite 2cos3xcos2x as a sum of trig…

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Q: Evaluate dx J x[(lnx)² + 9]

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Q: Let f(x) = 7 sin(x +7)+ cos 2x. Compute f(13) (0).

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