What is the integral from 0 to 1 of e^{3x-2} ?

The integral from 0 to 1 of e^{3x-2} is (e^3-1)/(3e^2)

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integral from 0 to 1 of e^{3x-2}

\int_{0}^{1} e^{3 x - 2} d x

\frac{e ^{3} - 1}{3 e ^{2}}

Decimal

0.86098 \dots

Solution steps

\int_{0}^{1} e^{3 x - 2} d x

Apply u-substitution

: \int_{- 2}^{1} e^{u} \frac{1}{3} d u

= \int_{- 2}^{1} e^{u} \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{- 2}^{1} e^{u} d u

Use the common integral:

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

= \frac{1}{3} [e^{u}]_{- 2}^{1}

Compute the boundaries:

e - \frac{1}{e ^{2}}

= \frac{1}{3} (e - \frac{1}{e ^{2}})

Simplify

= \frac{e ^{3} - 1}{3 e ^{2}}

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What is the integral from 0 to 1 of e^{3x-2} ?
The integral from 0 to 1 of e^{3x-2} is (e^3-1)/(3e^2)