Use the trapezium rule with 5 ordinates ( $h=0.25$ ) to find an approximate value of $\displaystyle\int_0^1x^2e^x\,dx$ , to 2 d.p.

Model answer

0.76

Also accepted: 0.7606, 0.761

Explanation: With

y_0=0

y_1\approx0.08025

y_2\approx0.41218

y_3\approx1.19081

y_4\approx2.71828

\dfrac{h}2[y_0+y_4+2(y_1+y_2+y_3)]\approx0.76

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

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