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

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

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

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

1

Solution steps

\int_{0}^{1} \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 d x

Apply the Power Rule

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

Compute the boundaries:

\frac{2}{3}

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

Simplify

= 1

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