Use the fact that sin ? =???−?−??/ 2?( e raised to the power i t minus e raised to the power negative i t divided by 2i ) to evaluate ∫ ?2?sin 3??? ( e is raised to the 2 theta) without “looping”. Be sure to convert back to an expression involving real values only. Confirm that both methods produce the same result.

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A: I am attaching image so that you understand each and every step.

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Q: Consider the following functions. X f(x) g(x) = x + 1 Find (fog)(x). Find the domain of (fog)(x).…

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A: Solution:-

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A: Here is the solution

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Q: 15. f(t) = 1 + cosh 5t

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Q: 11. f(x) = a sinx - b cos x + c

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A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…