Differentiate $\mathrm{e}^{\cos 2x}$ with respect to $x$.[2] Hence, find the exact value of \(\d

Question

Differentiate $\mathrm{e}^{\cos 2x}$ with respect to $x$.[2] Hence, find the exact value of $\displaystyle\int_{\tfrac{1}{4}\pi}^{\tfrac{1}{2}\pi}\mathrm{e}^{\cos 2x}\sin 4x\,\mathrm{d}x$.[5]

Accepted Answer

(a) $-2\sin 2x\,\mathrm{e}^{\cos 2x}$ (b) $\dfrac{2}{\mathrm{e}}-1$

N2026 P1 Q7

N2026 P1 Q7