What is the integral from pi/2 to pi of cos(x)+2 ?

The integral from pi/2 to pi of cos(x)+2 is -1+pi

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integral from pi/2 to pi of cos(x)+2

\int_{\frac{π}{2}}^{π} cos (x) + 2 d x

- 1 + π

Decimal

2.14159 \dots

Solution steps

\int_{\frac{π}{2}}^{π} cos (x) + 2 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_{\frac{π}{2}}^{π} cos (x) d x + \int_{\frac{π}{2}}^{π} 2 d x

\int_{\frac{π}{2}}^{π} cos (x) d x = - 1

\int_{\frac{π}{2}}^{π} 2 d x = π

= - 1 + π

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What is the integral from pi/2 to pi of cos(x)+2 ?
The integral from pi/2 to pi of cos(x)+2 is -1+pi