What is the integral from 1 to 2 of y*(2y)/3 ?

The integral from 1 to 2 of y*(2y)/3 is 14/9

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integral from 1 to 2 of y*(2y)/3

\int_{1}^{2} y \cdot \frac{2 y}{3} d y

\frac{14}{9}

Decimal Notation

1.55555 \dots

Solution steps

\int_{1}^{2} y \frac{2 y}{3} d y

Take the constant out:

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

= \frac{2}{3} \cdot \int_{1}^{2} yy d y

Simplify

yy : y^{2}

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{7}{3}

= \frac{2}{3} \cdot \frac{7}{3}

Simplify

= \frac{14}{9}

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What is the integral from 1 to 2 of y*(2y)/3 ?
The integral from 1 to 2 of y*(2y)/3 is 14/9