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

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

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

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

2 (e^{4} - e^{2})

Decimal

94.41818 \dots

Solution steps

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

Take the constant out:

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

= 4 \cdot \int_{1}^{2} e^{2 x} d x

Apply u-substitution

: \int_{2}^{4} e^{u} \frac{1}{2} d u

= 4 \cdot \int_{2}^{4} e^{u} \frac{1}{2} d u

Take the constant out:

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

= 4 \cdot \frac{1}{2} \cdot \int_{2}^{4} e^{u} d u

Use the common integral:

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

= 4 \cdot \frac{1}{2} [e^{u}]_{2}^{4}

Simplify

4 \cdot \frac{1}{2} [e^{u}]_{2}^{4} : 2 [e^{u}]_{2}^{4}

= 2 [e^{u}]_{2}^{4}

Compute the boundaries:

e^{4} - e^{2}

= 2 (e^{4} - e^{2})

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