First slide

Introduction to integration

Question

$\int \cos 4 xcos 7 xdx$ is equal to

Easy

A

$\sin 3 x + \sin 11 x + C$
B

$\frac{\sin 3 x}{3} + \frac{\sin 11 x}{11} + C$
C

$\frac{\sin 3 x}{6} + \frac{\sin 11 x}{22} + C$
D

None of these

Solution

Let $I = \int \cos 4 xcos 7 xdx$
Here, $\cos 4 xcos 7 x = \frac{1}{2} (\cos 3 x + \cos 11 x)$
$\begin{array}{l} ∴ l = \int \cos 4 xcos 7 xdx \\ = \frac{1}{2} \int (\cos 3 x + \cos 11 x) dx \\ = \frac{1}{2} \int \cos 3 xdx + \frac{1}{2} \int \cos 11 xdx \\ = \frac{\sin 3 x}{6} + \frac{\sin 11 x}{22} + C \end{array}$

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