What is the integral from 0 to a of xe^{x/a} ?

The integral from 0 to a of xe^{x/a} is a^2

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integral from 0 to a of xe^{x/a}

\int_{0}^{a} x e^{\frac{x}{a}} d x

a^{2}

Solution steps

\int_{0}^{a} x e^{\frac{x}{a}} d x

Apply Integration By Parts

: [a e^{\frac{x}{a}} x - \int a e^{\frac{x}{a}} d x]_{0}^{a}

= [a e^{\frac{x}{a}} x - \int a e^{\frac{x}{a}} d x]_{0}^{a}

\int a e^{\frac{x}{a}} d x = a^{2} e^{\frac{x}{a}}

= [a e^{\frac{x}{a}} x - a^{2} e^{\frac{x}{a}}]_{0}^{a}

Compute the boundaries:

a^{2}

= a^{2}

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What is the integral from 0 to a of xe^{x/a} ?
The integral from 0 to a of xe^{x/a} is a^2