Evaluate ∫ 2sin 5xsin x dx.

Question 43

HardOriginal question

Evaluate $\int 2\sin 5x\sin x\,dx$ .

\frac{\sin 4x}{4} - \frac{\sin 6x}{6} + C

Correct answerYour answer

\frac{\sin 4x}{4} + \frac{\sin 6x}{6} + C

Correct answerYour answer

\frac{\sin 6x}{6} - \frac{\sin 4x}{4} + C

Correct answerYour answer

\sin 4x - \sin 6x + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$2\sin A\sin B = \cos(A - B) - \cos(A + B)$ : $2\sin 5x\sin x = \cos 4x - \cos 6x$ .
$\int (\cos 4x - \cos 6x)\,dx = \frac{\sin 4x}{4} - \frac{\sin 6x}{6} + C$ .

Worth noting

A plus sign between the terms uses the cosine product formula, $2\cos A\cos B$ , instead.

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