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

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

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

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

\frac{1}{3}

Solution steps

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

Take the constant out:

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

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

Simplify

\frac{x}{x} : x

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{2}{3}

= \frac{1}{2} \cdot \frac{2}{3}

Simplify

= \frac{1}{3}

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