What is the integral from 0 to y of e^{x/y} ?

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

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integral from 0 to y of e^{x/y}

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

y (e - 1)

Solution steps

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

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

Compute the boundaries:

e - 1

= y (e - 1)

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