## Calculus: Early Transcendentals 8th Edition

$\displaystyle\int\limits_{\pi/4}^{\pi/3}\csc^{2}\theta d\theta=\dfrac{3-\sqrt{3}}{3}$
$\displaystyle\int\limits_{\pi/4}^{\pi/3}\csc^{2}\theta d\theta$ Integrate the expression directly and apply the second part of the fundamental theorem of calculus to get the answer: $\displaystyle\int\limits_{\pi/4}^{\pi/3}\csc^{2}\theta d\theta=\cot\theta\Big|_{\pi/4}^{\pi/3}=\cot\dfrac{\pi}{4}-\cot\dfrac{\pi}{3}=1-\dfrac{\sqrt{3}}{3}=\dfrac{3-\sqrt{3}}{3}$