What is the integral from-pi/2 to pi/2 of cos(x)-5 ?

The integral from-pi/2 to pi/2 of cos(x)-5 is 2-5pi

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integral from-pi/2 to pi/2 of cos(x)-5

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) - 5 d x

2 - 5 π

Decimal

- 13.70796 \dots

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) - 5 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}}^{\frac{π}{2}} cos (x) d x - \int_{- \frac{π}{2}}^{\frac{π}{2}} 5 d x

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

\int_{- \frac{π}{2}}^{\frac{π}{2}} 5 d x = 5 π

= 2 - 5 π

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What is the integral from-pi/2 to pi/2 of cos(x)-5 ?
The integral from-pi/2 to pi/2 of cos(x)-5 is 2-5pi