 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/17/a/ii/solution

The difference and sum of the two antiderivatives in part (i) give

\int e^{x} (sin x - cos x) d x = - e^{x} cos x + C,

and

\int e^{x} (sin x + cos x) d x = e^{x} sin x + C .

Their derivatives also verify the signs immediately.

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