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

The integral from 0 to pi/2 of 2x is (pi^2)/4

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integral from 0 to pi/2 of 2x

\int_{0}^{\frac{π}{2}} 2 x d x

\frac{π ^{2}}{4}

Decimal

2.46740 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 2 x d x

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{π ^{2}}{8}

= 2 \cdot \frac{π ^{2}}{8}

Simplify

= \frac{π ^{2}}{4}

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What is the integral from 0 to pi/2 of 2x ?
The integral from 0 to pi/2 of 2x is (pi^2)/4