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

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

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

\int_{0}^{π} - x cos (x) + x d x

2 + \frac{π ^{2}}{2}

Decimal

6.93480 \dots

Solution steps

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

\int_{0}^{π} x cos (x) d x = - 2

\int_{0}^{π} x d x = \frac{π ^{2}}{2}

= - (- 2) + \frac{π ^{2}}{2}

Simplify

= 2 + \frac{π ^{2}}{2}

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