What is the integral from-1 to 2 of e^{5x-4} ?

The integral from-1 to 2 of e^{5x-4} is (e^{15}-1)/(5e^9)

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integral from-1 to 2 of e^{5x-4}

\int_{- 1}^{2} e^{5 x - 4} d x

\frac{e ^{15} - 1}{5 e ^{9}}

Decimal

80.68573 \dots

Solution steps

\int_{- 1}^{2} e^{5 x - 4} d x

Apply u-substitution

: \int_{- 9}^{6} e^{u} \frac{1}{5} d u

= \int_{- 9}^{6} e^{u} \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{- 9}^{6} e^{u} d u

Use the common integral:

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

= \frac{1}{5} [e^{u}]_{- 9}^{6}

Compute the boundaries:

e^{6} - \frac{1}{e ^{9}}

= \frac{1}{5} (e^{6} - \frac{1}{e ^{9}})

Simplify

= \frac{e ^{15} - 1}{5 e ^{9}}

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What is the integral from-1 to 2 of e^{5x-4} ?
The integral from-1 to 2 of e^{5x-4} is (e^{15}-1)/(5e^9)