What is the integral from 0 to pi of cos(x)cos(2x) ?

The integral from 0 to pi of cos(x)cos(2x) is 0

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integral from 0 to pi of cos(x)cos(2x)

\int_{0}^{π} cos (x) cos (2 x) d x

0

Solution steps

\int_{0}^{π} cos (x) cos (2 x) d x

Apply Integration By Parts

: [cos (2 x) sin (x) - \int - 2 sin (2 x) sin (x) d x]_{0}^{π}

= [cos (2 x) sin (x) - \int - 2 sin (2 x) sin (x) d x]_{0}^{π}

\int - 2 sin (2 x) sin (x) d x = - \frac{4}{3} sin^{3} (x)

= [cos (2 x) sin (x) - (- \frac{4}{3} sin^{3} (x))]_{0}^{π}

Simplify

[cos (2 x) sin (x) - (- \frac{4}{3} sin^{3} (x))]_{0}^{π} : [\frac{1}{3} (3 cos (2 x) sin (x) + 4 sin^{3} (x))]_{0}^{π}

= [\frac{1}{3} (3 cos (2 x) sin (x) + 4 sin^{3} (x))]_{0}^{π}

Compute the boundaries:

0

= 0

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\int_{0}^{x} \frac{1}{2} d x

What is the integral from 0 to pi of cos(x)cos(2x) ?
The integral from 0 to pi of cos(x)cos(2x) is 0