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

Popular >

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

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

\frac{1}{3}

Decimal Notation

0.33333 \dots

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}

\int_{1}^{3} \frac{1}{( x - 2 ) ^{\frac{5}{3}}} d x

\int_{0}^{π} 5 + sin (x) d x

\int_{3 π}^{4 π} cos (\frac{1}{2} x) d x

\int_{- 1}^{1} (5 x + 5) d x

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

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