What is the integral from 0 to sqrt(y of)xe^{y^2} ?

The integral from 0 to sqrt(y of)xe^{y^2} is (ye^{y^2})/2

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integral from 0 to sqrt(y of)xe^{y^2}

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

\frac{y e ^{y^{2}}}{2}

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{y^{2}} \cdot \int_{0}^{y} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{y}

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

Compute the boundaries:

\frac{y}{2}

= e^{y^{2}} \frac{y}{2}

Simplify

= \frac{y e ^{y^{2}}}{2}

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What is the integral from 0 to sqrt(y of)xe^{y^2} ?
The integral from 0 to sqrt(y of)xe^{y^2} is (ye^{y^2})/2