First slide

Evaluation of definite integrals

Question

$\int_{0}^{π / 2} \frac{5 \tan x - 3 \cot x}{\tan x + \cot x} d x =$

Easy

A

$\frac{π}{2}$
B

$2 π$
C

$π$
D

$\frac{π}{4}$

Solution

$I = \int_{0}^{π / 2} \frac{5 T a n x - 3 C o t x}{T a n x + C o s x} d x (\sin c e \int_{0}^{π / 2} \frac{a T a n x + b C o t x}{T a n x + C o s x} d x = \frac{a + b}{4})$
$= (5 - 3) \frac{π}{4} = \frac{π}{2}$

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