What is the integral from 0 to pi of 9sin^4(x) ?

The integral from 0 to pi of 9sin^4(x) is (27pi)/8

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integral from 0 to pi of 9sin^4(x)

\int_{0}^{π} 9 sin^{4} (x) d x

\frac{27 π}{8}

Decimal Notation

10.60287 \dots

Solution steps

\int_{0}^{π} 9 sin^{4} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int_{0}^{π} sin^{4} (x) d x

Apply Integral Reduction

= 9 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \int_{0}^{π} sin^{2} (x) d x)

\int_{0}^{π} sin^{2} (x) d x = \frac{π}{2}

= 9 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2})

Simplify

9 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2}) : 9 (- [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8})

= 9 (- [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8})

Compute the boundaries:

0

= 9 (- 0 + \frac{3 π}{8})

Simplify

= \frac{27 π}{8}

y = (cos (7 x))^{x}

\frac{x + 6}{5}, ∣ x ∣

40 ln (3 x + 1)

\frac{1}{2} (e^{x} + e^{- x})

x^{2} - x - 6, - 4

What is the integral from 0 to pi of 9sin^4(x) ?
The integral from 0 to pi of 9sin^4(x) is (27pi)/8