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

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

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

\int_{0}^{π} x - sin (x) d x

\frac{π ^{2}}{2} - 2

Decimal

2.93480 \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{π ^{2}}{2}

\int_{0}^{π} sin (x) d x = 2

= \frac{π ^{2}}{2} - 2

\int_{- r}^{r} r^{2} - x^{2} d x

\int_{1}^{- x} 1 + t^{2} d t

\int_{- 3}^{3} 18 - x^{2} d x

\int_{0}^{1} e^{- s t} (t - 1) d t

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

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