What is the integral from 0 to 2pi of sin^4(x) ?

The integral from 0 to 2pi of sin^4(x) is (3pi)/4

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integral from 0 to 2pi of sin^4(x)

\int_{0}^{2 π} sin^{4} (x) d x

\frac{3 π}{4}

Decimal

2.35619 \dots

Solution steps

\int_{0}^{2 π} sin^{4} (x) d x

Apply Integral Reduction

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

\int_{0}^{2 π} sin^{2} (x) d x = π

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

Compute the boundaries:

0

= - 0 + \frac{3}{4} π

Simplify

= \frac{3 π}{4}

\frac{d}{d x} (sin (9 x) + (sin (9 x))^{2})

f (2 x) = 5 x - 3

\frac{\partial}{\partial x} (x + y)

(t + y + 1) d t - d y = 0

f (x) = 2 x - 4

What is the integral from 0 to 2pi of sin^4(x) ?
The integral from 0 to 2pi of sin^4(x) is (3pi)/4