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

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

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

\int_{\frac{π}{2}}^{π} 5 cos (x) d x

- 5

Solution steps

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

Use the common integral:

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

= 5 [sin (x)]_{\frac{π}{2}}^{π}

Compute the boundaries:

- 1

= 5 (- 1)

Simplify

= - 5

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