First slide

Introduction to integration

Question

$\int \frac{\cos 2 x - \cos 2 θ}{\cos x - \cos θ} d x is equal to$

Easy

A

$2 (\sin x + x \cos θ) + C$
B

$2 (\sin x - x \cos θ) + C$
C

$2 (\sin x + 2 x \cos θ) + C$
D

$2 (\sin x - 2 x \cos θ) + C$

Solution

$\int \frac{\cos 2 x - \cos 2 θ}{\cos x - \cos θ} dθ = \int \frac{2 \cos^{2} x - 1 - (2 \cos^{2} θ - 1)}{\cos x - \cos θ} dθ$
$\begin{aligned} = 2 \int \frac{\cos^{2} x - \cos^{2} θ}{\cos x - \cos θ} dθ \\ = 2 \int (\cos x + \cos θ) dθ \\ = 2 \sin x + 2 xcos θ + C \end{aligned}$

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