What is the integral from pi/2 to pi of 4sin(x) ?

The integral from pi/2 to pi of 4sin(x) is 4

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integral from pi/2 to pi of 4sin(x)

\int_{\frac{π}{2}}^{π} 4 sin (x) d x

4

Solution steps

\int_{\frac{π}{2}}^{π} 4 sin (x) d x

Take the constant out:

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

= 4 \cdot \int_{\frac{π}{2}}^{π} sin (x) d x

Use the common integral:

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

= 4 [- cos (x)]_{\frac{π}{2}}^{π}

Compute the boundaries:

1

= 4 \cdot 1

Simplify

= 4

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What is the integral from pi/2 to pi of 4sin(x) ?
The integral from pi/2 to pi of 4sin(x) is 4