What is the integral from 0 to 3 of e^{x/3} ?

The integral from 0 to 3 of e^{x/3} is 3(e-1)

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integral from 0 to 3 of e^{x/3}

\int_{0}^{3} e^{\frac{x}{3}} d x

3 (e - 1)

Decimal

5.15484 \dots

Solution steps

\int_{0}^{3} e^{\frac{x}{3}} d x

Apply u-substitution

: \int_{0}^{1} e^{u} \cdot 3 d u

= \int_{0}^{1} e^{u} \cdot 3 d u

Take the constant out:

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

= 3 \cdot \int_{0}^{1} e^{u} d u

Use the common integral:

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

= 3 [e^{u}]_{0}^{1}

Compute the boundaries:

e - 1

= 3 (e - 1)

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What is the integral from 0 to 3 of e^{x/3} ?
The integral from 0 to 3 of e^{x/3} is 3(e-1)