What is the integral from 0 to pi of 10sin^4(x) ?

The integral from 0 to pi of 10sin^4(x) is (15pi)/4

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integral from 0 to pi of 10sin^4(x)

\int_{0}^{π} 10 sin^{4} (x) d x

\frac{15 π}{4}

Decimal

11.78097 \dots

Solution steps

\int_{0}^{π} 10 sin^{4} (x) d x

Take the constant out:

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

= 10 \cdot \int_{0}^{π} sin^{4} (x) d x

Apply Integral Reduction

= 10 (- [\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}

= 10 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2})

Simplify

10 (- [\frac{cos ( x ) sin ^{3} ( x )}{4}]_{0}^{π} + \frac{3}{4} \cdot \frac{π}{2}) : 10 (- [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8})

= 10 (- [\frac{1}{4} sin^{3} (x) cos (x)]_{0}^{π} + \frac{3 π}{8})

Compute the boundaries:

0

= 10 (- 0 + \frac{3 π}{8})

Simplify

= \frac{15 π}{4}

\int \frac{17}{x ^{2} + 1} d x

y^{^{''}} - 8 y^{^{'}} + 32 y = 0

5 x (x - 1)

\int 2.4

x \to 0 lim (\frac{( ln ( x ) )}{x})

What is the integral from 0 to pi of 10sin^4(x) ?
The integral from 0 to pi of 10sin^4(x) is (15pi)/4