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

The integral from-pi to pi of sin^4(x) is (3pi)/4

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integral from-pi to pi of sin^4(x)

\int_{- π}^{π} sin^{4} (x) d x

\frac{3 π}{4}

Decimal

2.35619 \dots

Solution steps

\int_{- π}^{π} sin^{4} (x) d x

Apply Integral Reduction

= - [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{- π}^{π} + \frac{3}{4} \cdot \int_{- π}^{π} sin^{2} (x) d x

\int_{- π}^{π} sin^{2} (x) d x = π

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

Compute the boundaries:

0

= - 0 + \frac{3}{4} π

Simplify

= \frac{3 π}{4}

What is the integral from-pi to pi of sin^4(x) ?
The integral from-pi to pi of sin^4(x) is (3pi)/4