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

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

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

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

- 5

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

\int cos (x) d x = sin (x)

= - 5 [sin (x)]_{- \frac{5 π}{2}}^{- 2 π}

Compute the boundaries:

1

= - 5 \cdot 1

Simplify

= - 5

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