First slide

Evaluation of definite integrals

Question

$\int_{0}^{1} \sqrt{\frac{1 - x}{1 + x}} d x$

Easy

A

$\frac{π}{2} + 1$
B

$\frac{π}{2} - 1$
C

–1
D

1

Solution

$\int_{0}^{1} \sqrt{\frac{1 - x}{1 + x}} d x = \int_{0}^{1} \frac{1 - x}{1 + x^{2}} d x, x = \sin θ$
$= \int_{0}^{\frac{π}{2}} (1 - \sin θ) d θ = \frac{π}{2} - 1$

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