First slide

Introduction to integration

Question

$\int \frac{\cos 2 x - \cos 2 θ}{\cos x - \cos θ} d x =$

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

$\int \frac{\cos 2 x - \cos 2 θ}{\cos x - \cos θ} d x$
$= \int \frac{(2 \cos^{2} x - 1) - (2 \cos^{2} θ - 1)}{\cos x - \cos θ} d x$
$= 2 \int \frac{\cos^{2} x - \cos^{2} θ}{\cos x - \cos θ} d x$
$= 2 \int (\cos x + \cos θ) + C$
= $2 (\int \cos x d x + \int \cos θ d x)$
$= 2 (\sin x + \cos θ . x) + C$

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