What is the integral from 2 to 3 of 4e^{4x} ?

The integral from 2 to 3 of 4e^{4x} is e^{12}-e^8

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integral from 2 to 3 of 4e^{4x}

\int_{2}^{3} 4 e^{4 x} d x

e^{12} - e^{8}

Decimal Notation

159773.83343 \dots

Solution steps

\int_{2}^{3} 4 e^{4 x} d x

Take the constant out:

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

= 4 \cdot \int_{2}^{3} e^{4 x} d x

Apply u-substitution

: \int_{8}^{12} e^{u} \frac{1}{4} d u

= 4 \cdot \int_{8}^{12} 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

= 4 \cdot \frac{1}{4} \cdot \int_{8}^{12} e^{u} d u

Use the common integral:

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

= 4 \cdot \frac{1}{4} [e^{u}]_{8}^{12}

Simplify

4 \cdot \frac{1}{4} [e^{u}]_{8}^{12} : [e^{u}]_{8}^{12}

= [e^{u}]_{8}^{12}

Compute the boundaries:

e^{12} - e^{8}

= e^{12} - e^{8}

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What is the integral from 2 to 3 of 4e^{4x} ?
The integral from 2 to 3 of 4e^{4x} is e^{12}-e^8