What is the integral from-pi/2 to pi/2 of (cos(x)-3) ?

The integral from-pi/2 to pi/2 of (cos(x)-3) is 2-3pi

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integral from-pi/2 to pi/2 of (cos(x)-3)

\int_{- \frac{π}{2}}^{\frac{π}{2}} (cos (x) - 3) d x

2 - 3 π

Decimal

- 7.42477 \dots

Solution steps

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) - 3 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}} 3 d x

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

\int_{- \frac{π}{2}}^{\frac{π}{2}} 3 d x = 3 π

= 2 - 3 π

What is the integral from-pi/2 to pi/2 of (cos(x)-3) ?
The integral from-pi/2 to pi/2 of (cos(x)-3) is 2-3pi