First slide

Evaluation of definite integrals

Question

$\int_{0}^{π / 2} \frac{1}{1 + \tan^{3} x} d x =$

Easy

A

$π$
B

$\frac{π}{4}$
C

$\frac{π}{2}$
D

$2 π$

Solution

$\int_{0}^{π / 2} \frac{1}{1 + T a n^{3} x} d x = \int_{0}^{π / 2} \frac{C o s^{3} x}{S i n^{3} x + C o s^{3} x} d x = \frac{π}{4} (\sin c e \int_{0}^{\frac{π}{2}} \frac{f (C o s^{} x)}{f (C o s^{} x) + f (\sin^{} x)} d x = \frac{π}{4})$

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