Evaluate - - sin4x - sin8x dx-

∫sin 4 x sin 8 x d x=12∫ (2sin 4 xsin 8 x )d x=12∫ (cos 4 x cos 12 x)d x=12∫cos 4 x d x 12∫cos 12 x d x #160; #160; #160; #160; #160; #16 ...

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Byju's Answer

Standard XII

Mathematics

Many-One onto Function

Evaluate : ...

Question

Evaluate : $\int s i n 4 x . s i n 8 x d x$ .

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Solution

$\int sin 4 x sin 8 x d x = \frac{1}{2} \int (2 sin 4 x sin 8 x) d x = \frac{1}{2} \int (cos 4 x - cos 12 x) d x = \frac{1}{2} \int cos 4 x d x - \frac{1}{2} \int cos 12 x d x$
$= \frac{sin 4 x}{8} - \frac{sin 12 x}{24} + C$

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Evaluate : ∫sin4x.sin8xdx.

∫sin4xsin8xdx=12∫(2sin4xsin8x)dx=12∫(cos4x−cos12x)dx=12∫cos4xdx−12∫cos12xdx =sin4x8−sin12x24+C

Evaluate : $\int s i n 4 x . s i n 8 x d x$ .

$\int sin 4 x sin 8 x d x = \frac{1}{2} \int (2 sin 4 x sin 8 x) d x = \frac{1}{2} \int (cos 4 x - cos 12 x) d x = \frac{1}{2} \int cos 4 x d x - \frac{1}{2} \int cos 12 x d x$
$= \frac{sin 4 x}{8} - \frac{sin 12 x}{24} + C$