What is the integral from 0 to 1/2 of 2x^2 ?

The integral from 0 to 1/2 of 2x^2 is 1/12

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integral from 0 to 1/2 of 2x^2

\int_{0}^{\frac{1}{2}} 2 x^{2} d x

\frac{1}{12}

Decimal

0.08333 \dots

Solution steps

\int_{0}^{\frac{1}{2}} 2 x^{2} 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{1}{2}} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{\frac{1}{2}}

= 2 [\frac{x ^{3}}{3}]_{0}^{\frac{1}{2}}

Compute the boundaries:

\frac{1}{24}

= 2 \cdot \frac{1}{24}

Simplify

= \frac{1}{12}

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What is the integral from 0 to 1/2 of 2x^2 ?
The integral from 0 to 1/2 of 2x^2 is 1/12