What is the integral from 0 to pi of 1/2 sin(x) ?

The integral from 0 to pi of 1/2 sin(x) is 1

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integral from 0 to pi of 1/2 sin(x)

\int_{0}^{π} \frac{1}{2} sin (x) d x

1

Solution steps

\int_{0}^{π} \frac{1}{2} sin (x) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{π} sin (x) d x

Use the common integral:

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

= \frac{1}{2} [- cos (x)]_{0}^{π}

Compute the boundaries:

2

= \frac{1}{2} \cdot 2

Simplify

= 1

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What is the integral from 0 to pi of 1/2 sin(x) ?
The integral from 0 to pi of 1/2 sin(x) is 1