Evaluate the exact value of $\displaystyle\int_0^1x^2e^x\,dx$ using integration by parts.

Model answer

e-2

Also accepted: 0.72, 0.718

Explanation: With

u=x^2

dv=e^x\,dx

\int x^2e^x\,dx=x^2e^x-2xe^x+2e^x+C

. Evaluating from 0 to 1 gives

e-2\approx0.71828

Derived from ZIMSEC Pure Mathematics Paper 2, November 2025, Q10

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