What is the integral from 0 to pi of sqrt(x)-sin(x) ?

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

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integral from 0 to pi of sqrt(x)-sin(x)

\int_{0}^{π} x - sin (x) d x

\frac{2 π ^{\frac{3}{2}}}{3} - 2

Decimal

1.71221 \dots

Solution steps

\int_{0}^{π} x - sin (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} x d x - \int_{0}^{π} sin (x) d x

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

\int_{0}^{π} sin (x) d x = 2

= \frac{2 π ^{\frac{3}{2}}}{3} - 2

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