First slide

Methods of integration

Question

The value of $\int \frac{\sin α}{\sqrt{1 + \cos α}} d α$ is

Easy

A

$2 \sqrt{2} \cos (α / 2) + C$
B

$- 2 \sqrt{2} \cos (α / 2) + C$
C

$\sqrt{2} \cos (α / 2) + C$
D

$- \sqrt{2} \cos (α / 2) + C$

Solution

$\begin{array}{l} \int \frac{\sin α}{\sqrt{1 + \cos α}} d α = - \int \frac{d x}{\sqrt{x}} (x = 1 + \cos α) \\ = - 2 (1 + \cos α)^{1 / 2} + C \\ = - 2 \sqrt{2} \cos α / 2 + C . \end{array}$

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