What is the integral from 0 to 1 of y*2y ?

The integral from 0 to 1 of y*2y is 2/3

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integral from 0 to 1 of y*2y

\int_{0}^{1} y \cdot 2 y d y

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

\int_{0}^{1} y \cdot 2 y d y

Take the constant out:

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

= 2 \cdot \int_{0}^{1} yy d y

Simplify

yy : y^{2}

= 2 \cdot \int_{0}^{1} y^{2} d y

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{3}

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

Simplify

= \frac{2}{3}

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