First slide

Evaluation of definite integrals

Question

$\int_{0}^{π / 2} \frac{\sin^{2} x - \cos^{2} x}{\sin^{3} x + \cos^{3} x} d x =$

Easy

A

0
B

1
C

$\frac{π}{4}$
D

$-$ 1

Solution

$I = \int_{0}^{π / 2} \frac{S i n^{2} x - C o s^{2} x}{S i n^{3} x + C o s^{3} x} d x__________(1)$
$I = \int_{0}^{π / 2} \frac{C o s^{2} x - S i n^{2} x}{S i n^{3} x + C o s^{3} x} d x__________(2)$

$(1) + (2) \Rightarrow 2 I = \int_{0}^{π / 2} 0 d x = 0 \Rightarrow I = 0$

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