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  4. The value of the definite integral ∫ limits0π / 2( cos 10 x ⋅ sin 12 x) d x, is equal to

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Q. The value of the definite integral $\int\limits_0^{\pi / 2}\left(\cos ^{10} x \cdot \sin 12 x\right) d x$, is equal to

Integrals

Solution:

$\int\limits_0^{\pi / 2}\left(\cos ^{10} x \cdot \sin (11 x+x)\right) d x$ expand and use by parts.