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

The integral from 0 to 1/2 of e^{sqrt(2x)} is 1

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integral from 0 to 1/2 of e^{sqrt(2x)}

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

1

Solution steps

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

Apply u-substitution

: \int_{0}^{1} e^{u} u d u

= \int_{0}^{1} e^{u} u d u

Apply Integration By Parts

: [e^{u} u - \int e^{u} d u]_{0}^{1}

= [e^{u} u - \int e^{u} d u]_{0}^{1}

\int e^{u} d u = e^{u}

= [e^{u} u - e^{u}]_{0}^{1}

Compute the boundaries:

1

= 1

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What is the integral from 0 to 1/2 of e^{sqrt(2x)} ?
The integral from 0 to 1/2 of e^{sqrt(2x)} is 1