What is the integral from 0 to infinity of x^{1/2} ?

The integral from 0 to infinity of x^{1/2} is diverges

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integral from 0 to infinity of x^{1/2}

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

diverges

Solution steps

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

Compute the indefinite integral:

\int x^{\frac{1}{2}} d x = \frac{2}{3} x^{\frac{3}{2}} + C

Compute the boundaries:

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

diverges

= diverges

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What is the integral from 0 to infinity of x^{1/2} ?
The integral from 0 to infinity of x^{1/2} is diverges