What is the integral from 0 to infinity of ue^{-u^2} ?

The integral from 0 to infinity of ue^{-u^2} is 1/2

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integral from 0 to infinity of ue^{-u^2}

\int_{0}^{\infty} u e^{- u^{2}} d u

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\int_{0}^{\infty} u e^{- u^{2}} d u

Compute the indefinite integral:

\int u e^{- u^{2}} d u = - \frac{1}{2} e^{- u^{2}} + C

Compute the boundaries:

\int_{0}^{\infty} u e^{- u^{2}} d u = 0 - (- \frac{1}{2})

= 0 - (- \frac{1}{2})

Simplify

= \frac{1}{2}

\frac{s}{s ^{2} + 10 s + 9.8}

\frac{d y}{d x} = 2 \cdot \frac{y}{x} + (\frac{y}{x})^{2}

x \to 1 + lim (\frac{ln ( x )}{x - 1})

x \to 0 lim (\frac{6}{x ^{2} + x} - \frac{6}{x})

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

What is the integral from 0 to infinity of ue^{-u^2} ?
The integral from 0 to infinity of ue^{-u^2} is 1/2