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

The integral from-2 to 2 of e^{4x} is (e^{16}-1)/(4e^8)

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

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

\frac{e ^{16} - 1}{4 e ^{8}}

Decimal

745.23941 \dots

Solution steps

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

Apply u-substitution

= \int_{- 8}^{8} e^{u} \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int_{- 8}^{8} e^{u} d u

Use the common integral:

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

= \frac{1}{4} [e^{u}]_{- 8}^{8}

Compute the boundaries:

e^{8} - \frac{1}{e ^{8}}

= \frac{1}{4} (e^{8} - \frac{1}{e ^{8}})

Simplify

= \frac{e ^{16} - 1}{4 e ^{8}}

What is the integral from-2 to 2 of e^{4x} ?
The integral from-2 to 2 of e^{4x} is (e^{16}-1)/(4e^8)