What is the integral from 0 to 1 of 2/3 x ?

The integral from 0 to 1 of 2/3 x is 1/3

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integral from 0 to 1 of 2/3 x

\int_{0}^{1} \frac{2}{3} x d x

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

\int_{0}^{1} \frac{2}{3} x d x

Take the constant out:

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

= \frac{2}{3} \cdot \int_{0}^{1} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{2}

= \frac{2}{3} \cdot \frac{1}{2}

Simplify

= \frac{1}{3}

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What is the integral from 0 to 1 of 2/3 x ?
The integral from 0 to 1 of 2/3 x is 1/3