What is the integral from 0 to 1 of sin^4(x)cos(x) ?

The integral from 0 to 1 of sin^4(x)cos(x) is (sin^5(1))/5

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integral from 0 to 1 of sin^4(x)cos(x)

\int_{0}^{1} sin^{4} (x) cos (x) d x

\frac{sin ^{5} ( 1 )}{5}

Decimal

0.08437 \dots

Solution steps

\int_{0}^{1} sin^{4} (x) cos (x) d x

Apply u-substitution

: \int_{0}^{s i n (1)} u^{4} d u

= \int_{0}^{s i n (1)} u^{4} d u

Apply the Power Rule

: [\frac{u ^{5}}{5}]_{0}^{s i n (1)}

= [\frac{u ^{5}}{5}]_{0}^{s i n (1)}

Compute the boundaries:

\frac{sin ^{5} ( 1 )}{5}

= \frac{sin ^{5} ( 1 )}{5}

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What is the integral from 0 to 1 of sin^4(x)cos(x) ?
The integral from 0 to 1 of sin^4(x)cos(x) is (sin^5(1))/5