Question
Evaluate: $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \cos x d x$
✓
Answer
$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \cos x d x=[\sin x]_{\frac{\pi}{6}}^{\frac{\pi}{3}}$
$=\sin \frac{\pi}{3}-\sin \frac{\pi}{6}$
$=\frac{\sqrt{3}}{2}-\frac{1}{2}$
$=\frac{\sqrt{3}-1}{2}$
$=\sin \frac{\pi}{3}-\sin \frac{\pi}{6}$
$=\frac{\sqrt{3}}{2}-\frac{1}{2}$
$=\frac{\sqrt{3}-1}{2}$
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