What is the integral from 0 to 3 of piy^{2/3} ?

The integral from 0 to 3 of piy^{2/3} is (9*3^{2/3}pi)/5

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integral from 0 to 3 of piy^{2/3}

\int_{0}^{3} π y^{\frac{2}{3}} d y

\frac{9 \cdot 3 ^{\frac{2}{3}} π}{5}

Decimal

11.76259 \dots

Solution steps

\int_{0}^{3} π y^{\frac{2}{3}} d y

Take the constant out:

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

= π \cdot \int_{0}^{3} y^{\frac{2}{3}} d y

Apply the Power Rule

: [\frac{3}{5} y^{\frac{5}{3}}]_{0}^{3}

= π [\frac{3}{5} y^{\frac{5}{3}}]_{0}^{3}

Compute the boundaries:

\frac{9 \cdot 3 ^{\frac{2}{3}}}{5}

= π \frac{9 \cdot 3 ^{\frac{2}{3}}}{5}

Simplify

= \frac{9 \cdot 3 ^{\frac{2}{3}} π}{5}

\int_{2 x}^{x^{5}} e^{- t^{2}} d t

\int_{1}^{3} \frac{x ^{3} + 4 x}{x ^{5}} d x

\int_{0}^{1} (2 x^{2} + 4 x + 1) d x

\int_{0}^{2 π} sin (x) sin (x) d x

\int_{0}^{4} \frac{1}{64 x ^{2} + 25} d x

What is the integral from 0 to 3 of piy^{2/3} ?
The integral from 0 to 3 of piy^{2/3} is (9*3^{2/3}pi)/5