What is the integral from-v to v of e^{u/v} ?

The integral from-v to v of e^{u/v} is v(e-1/e)

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integral from-v to v of e^{u/v}

\int_{- v}^{v} e^{\frac{u}{v}} d u

v (e - \frac{1}{e})

Solution steps

\int_{- v}^{v} e^{\frac{u}{v}} d u

Apply u-substitution

= \int_{- 1}^{1} e^{w} v d w

Take the constant out:

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

= v \cdot \int_{- 1}^{1} e^{w} d w

Use the common integral:

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

= v [e^{w}]_{- 1}^{1}

Compute the boundaries:

e - \frac{1}{e}

= v (e - \frac{1}{e})

What is the integral from-v to v of e^{u/v} ?
The integral from-v to v of e^{u/v} is v(e-1/e)