First slide

Evaluation of definite integrals

Question

The value of the integral $\int_{0}^{π / 4} \frac{\sin x + \cos x}{3 + \sin 2 x} d x$ is

Easy

A

log 2
B

log 3
C

(1/4) log 3
D

(1/8) log 3.

Solution

Put $\sin x - \cos x = t$ so that
$\begin{array}{l} I = \int_{- 1}^{0} \frac{d t}{3 + 1 - t^{2}} \\ {= \frac{1}{2 (2)} \log |\frac{2 + t}{2 - t}|]}_{- 1}^{0} = \frac{1}{4} \log 3 . \end{array}$

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