Find $\frac{\mathrm{d}}{\mathrm{d}x}\left(x \mathrm{e}^{\frac{1}{2}x}\right)$.[2] Hence evaluate \

Question

Find $\frac{\mathrm{d}}{\mathrm{d}x}\left(x \mathrm{e}^{\frac{1}{2}x}\right)$.[2] Hence evaluate $\int_{0}^{4} x \mathrm{e}^{\frac{1}{2}x} \, \mathrm{d}x$, leaving your answer in the form $k(\mathrm{e}^2 + 1)$, where $k$ is a constant to be found.[5]

Accepted Answer

(a) $\dfrac{1}{2}xe^{\frac{1}{2}x}+e^{\frac{1}{2}x}$ (b) $4(e^2+1)$, so $k=4$

(A Math) 2025 CCHY PRELIMS P1 Q3

(A Math) 2025 CCHY PRELIMS P1 Q3

Solution:

Solution locked