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

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

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integral from 0 to pi of (1-sin^3(θ))

\int_{0}^{π} (1 - sin^{3} (θ)) d θ

π - \frac{4}{3}

Decimal

1.80825 \dots

Solution steps

\int_{0}^{π} 1 - sin^{3} (θ) d θ

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 θ - \int_{0}^{π} sin^{3} (θ) d θ

\int_{0}^{π} 1 d θ = π

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

= π - \frac{4}{3}

\int_{- π}^{π} x sin (x) d x

\int_{0}^{π} sin^{3} (θ) d θ

\int_{0}^{π} (1 - sin^{3} (x)) d x

\int_{0}^{3} x + 3 d x

\int_{2}^{3} x^{4} + 3 x^{2} + 4 d x

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