What is the integral from 0 to pi/2 of 1-sin^3(x) ?

The integral from 0 to pi/2 of 1-sin^3(x) is pi/2-2/3

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integral from 0 to pi/2 of 1-sin^3(x)

\int_{0}^{\frac{π}{2}} 1 - sin^{3} (x) d x

\frac{π}{2} - \frac{2}{3}

Decimal Notation

0.90412 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 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}^{\frac{π}{2}} 1 d x - \int_{0}^{\frac{π}{2}} sin^{3} (x) d x

\int_{0}^{\frac{π}{2}} 1 d x = \frac{π}{2}

\int_{0}^{\frac{π}{2}} sin^{3} (x) d x = \frac{2}{3}

= \frac{π}{2} - \frac{2}{3}

\int_{0}^{1} x^{2} - 1 d x

\int_{0}^{4} ln (3 t + 1) d t

\int_{0}^{2} (x ln (x)) d x

\int_{1}^{\infty} \frac{8}{7 x - 1} d x

\int_{- \infty}^{0} x e^{- 5 x} d x

What is the integral from 0 to pi/2 of 1-sin^3(x) ?
The integral from 0 to pi/2 of 1-sin^3(x) is pi/2-2/3