What is the integral from 0 to pi of x+xcos(x) ?

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

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integral from 0 to pi of x+xcos(x)

\int_{0}^{π} x + x cos (x) d x

\frac{π ^{2}}{2} - 2

Decimal

2.93480 \dots

Solution steps

\int_{0}^{π} x + x cos (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} x cos (x) d x

\int_{0}^{π} x d x = \frac{π ^{2}}{2}

\int_{0}^{π} x cos (x) d x = - 2

= \frac{π ^{2}}{2} - 2

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