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 Notation

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_{2}^{3} x^{- 2} d x

\int_{1}^{x^{3}} \frac{1}{1 + t ^{4}} d t

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

\int_{- 3}^{3} ln (x + 4) d x

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

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