What is the integral from 0 to pi of x/pi ?

The integral from 0 to pi of x/pi is pi/2

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integral from 0 to pi of x/pi

\int_{0}^{π} \frac{x}{π} d x

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{0}^{π} \frac{x}{π} d x

Take the constant out:

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

= \frac{1}{π} \cdot \int_{0}^{π} x d x

Apply the Power Rule

= \frac{1}{π} [\frac{x ^{2}}{2}]_{0}^{π}

Compute the boundaries:

\frac{π ^{2}}{2}

= \frac{1}{π} \cdot \frac{π ^{2}}{2}

Simplify

= \frac{π}{2}

What is the integral from 0 to pi of x/pi ?
The integral from 0 to pi of x/pi is pi/2