What is the integral from 0 to pi of cos(x)sin^4(x) ?

The integral from 0 to pi of cos(x)sin^4(x) is 0

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integral from 0 to pi of cos(x)sin^4(x)

\int_{0}^{π} cos (x) sin^{4} (x) d x

0

Solution steps

\int_{0}^{π} cos (x) sin^{4} (x) d x

Compute the indefinite integral:

\int cos (x) sin^{4} (x) d x = \frac{sin ^{5} ( x )}{5} + C

Compute the boundaries:

\int_{0}^{π} cos (x) sin^{4} (x) d x = 0 - 0

= 0 - 0

Simplify

= 0

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\int_{0}^{1} \frac{1}{1 + y ^{2}} d y

\int_{0}^{2} \frac{1}{( 1 - 2 x ) ^{2}} d x

\int_{- 1}^{3} x^{2} - 2 x + 1 d x

\int_{0}^{x} t + t^{3} d x

What is the integral from 0 to pi of cos(x)sin^4(x) ?
The integral from 0 to pi of cos(x)sin^4(x) is 0