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

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

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integral from 0 to 2 of pi/2 r

\int_{0}^{2} \frac{π}{2} r d r

π

Decimal

3.14159 \dots

Solution steps

\int_{0}^{2} \frac{π}{2} r d r

Take the constant out:

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

= \frac{π}{2} \cdot \int_{0}^{2} r d r

Apply the Power Rule

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

Compute the boundaries:

2

= \frac{π}{2} \cdot 2

Simplify

= π

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