First slide

Evaluation of definite integrals

Question

$\int_{0}^{π / 2} \frac{1}{1 + 4 \sin^{2} x} d x =$

Easy

A

$\frac{π}{2 \sqrt{5}}$
B

$\frac{π}{\sqrt{5}}$
C

$2 π$
D

$\sqrt{5} π$

Solution

$\int_{0}^{π / 2} \frac{1}{C o s^{2} x + 5 S i n^{2} x} d x$ $= \frac{π}{2 a b} = \frac{π}{2.1 \sqrt{5}} = \frac{π}{2 \sqrt{5}}$

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