What is the integral from 0 to 1 of 5/2 y^{3/2} ?

The integral from 0 to 1 of 5/2 y^{3/2} is 1

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integral from 0 to 1 of 5/2 y^{3/2}

\int_{0}^{1} \frac{5}{2} y^{\frac{3}{2}} d y

1

Solution steps

\int_{0}^{1} \frac{5}{2} y^{\frac{3}{2}} d y

Take the constant out:

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

= \frac{5}{2} \cdot \int_{0}^{1} y^{\frac{3}{2}} d y

Apply the Power Rule

: [\frac{2}{5} y^{\frac{5}{2}}]_{0}^{1}

= \frac{5}{2} [\frac{2}{5} y^{\frac{5}{2}}]_{0}^{1}

Compute the boundaries:

\frac{2}{5}

= \frac{5}{2} \cdot \frac{2}{5}

Simplify

= 1

\int_{5}^{10} \frac{2}{5} - \frac{1}{25} x d x

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What is the integral from 0 to 1 of 5/2 y^{3/2} ?
The integral from 0 to 1 of 5/2 y^{3/2} is 1