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Moderate

Inverse Trig Integral

APCALC-XKRAVB

Evaluate the definite integral, $\int_{\frac{\pi }{2}}^{\pi }\cfrac{\sin(x)}{1+\cos^{2}x}dx$.

A

$\cfrac{\pi }{4}$

B

$-\cfrac{\pi }{4}$

C

$\cfrac{\pi }{2}$

D

$-\cfrac{\pi }{2}$