Show that $\sin(\pi-\theta)=\sin(\theta)$.[1] Find $\int e^x\sin x\,\mathrm{d}x$.[3] Use th

Question

Show that $\sin(\pi-\theta)=\sin(\theta)$.[1] Find $\int e^x\sin x\,\mathrm{d}x$.[3] Use the substitution $u=\pi-x$ and the results in parts (a) and (b) to find the exact value of $\int_{\frac{\pi}{2}}^{\pi} e^{\pi-x}\sin x\,\mathrm{d}x$.[4]

Accepted Answer

(a) $\sin(\pi-\theta)=\sin\theta$ (b) $\dfrac{e^x}{2}(\sin x-\cos x)+C$ (c) $\dfrac{e^{\frac{\pi}{2}}+1}{2}$.

2026 HCI Promo Q4

2026 HCI Promo Q4

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