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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-1/8/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / 8 / Solution by

Codex  0 2026-10-18

The integrand is a continuous function, so the fundamental theorem of calculus differentiates the upper limit directly:

\frac{d}{d x} \int_{0}^{x} e^{- y^{2}} sin y d y = e^{- x^{2}} sin x .

No explicit antiderivative is needed.

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