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

The integral from-(5pi)/2 to (5pi)/2 of (cos(x)-2) is 2-10pi

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

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

2 - 10 π

Decimal

- 29.41592 \dots

Solution steps

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

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

\int_{- \frac{5 π}{2}}^{\frac{5 π}{2}} 2 d x = 10 π

= 2 - 10 π

What is the integral from-(5pi)/2 to (5pi)/2 of (cos(x)-2) ?
The integral from-(5pi)/2 to (5pi)/2 of (cos(x)-2) is 2-10pi