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

The integral from 0 to 1 of x(3/2 sqrt(x)) is 3/5

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integral from 0 to 1 of x(3/2 sqrt(x))

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

\frac{3}{5}

Solution steps

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

Take the constant out:

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

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

Simplify

x x : x^{\frac{3}{2}}

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

Apply the Power Rule

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

= \frac{3}{2} [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{1}

Compute the boundaries:

\frac{2}{5}

= \frac{3}{2} \cdot \frac{2}{5}

Simplify

= \frac{3}{5}

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What is the integral from 0 to 1 of x(3/2 sqrt(x)) ?
The integral from 0 to 1 of x(3/2 sqrt(x)) is 3/5