What is the integral from 0 to pi of (1+sin^3(x)) ?

The integral from 0 to pi of (1+sin^3(x)) is pi+4/3

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integral from 0 to pi of (1+sin^3(x))

\int_{0}^{π} (1 + sin^{3} (x)) d x

π + \frac{4}{3}

Decimal

4.47492 \dots

Solution steps

\int_{0}^{π} 1 + sin^{3} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{π} 1 d x + \int_{0}^{π} sin^{3} (x) d x

\int_{0}^{π} 1 d x = π

\int_{0}^{π} sin^{3} (x) d x = \frac{4}{3}

= π + \frac{4}{3}

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\int_{0}^{4} \frac{2 x}{x ^{2} + 1} d x

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What is the integral from 0 to pi of (1+sin^3(x)) ?
The integral from 0 to pi of (1+sin^3(x)) is pi+4/3