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

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

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

\int_{- π}^{0} sin (x) + x d x

- 2 - \frac{π ^{2}}{2}

Decimal

- 6.93480 \dots

Solution steps

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

\int_{- π}^{0} sin (x) d x = - 2

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

= - 2 - \frac{π ^{2}}{2}

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