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

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

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

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

diverges

Solution steps

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

diverges

= diverges

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

\int_{- 1}^{1} t^{2} cos (nπ t) d t

\int_{- 1}^{2} \frac{1}{x + 2} d x

\int_{0}^{2} e^{x} d x

\int_{0}^{π} x sin^{5} (x) d x

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