First slide

Evaluation of definite integrals

Question

The value of $\int_{π / 4}^{π / 2} \cot θ {cosec}^{2} θ d θ$ is

Easy

A

$- \frac{1}{2}$
B

$\frac{1}{2}$
C

$\frac{1}{3}$
D

$- \frac{1}{3}$

Solution

$\begin{array}{l} \int_{π / 4}^{π / 2} \cot θ {cosec}^{2} θ d θ = - \int_{1}^{0} u d u (u = \cot θ) \\ = \int_{0}^{1} u d u = {\frac{u^{2}}{2}|}_{0}^{1} = \frac{1}{2} \end{array}$

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