What is the integral from 0 to 8 of 100e^{(1/4 x)} ?

The integral from 0 to 8 of 100e^{(1/4 x)} is 400(e^2-1)

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integral from 0 to 8 of 100e^{(1/4 x)}

\int_{0}^{8} 100 e^{(\frac{1}{4} x)} d x

400 (e^{2} - 1)

Decimal Notation

2555.62243 \dots

Solution steps

\int_{0}^{8} 100 e^{\frac{1}{4} x} d x

Take the constant out:

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

= 100 \cdot \int_{0}^{8} e^{\frac{1}{4} x} d x

Apply u-substitution

: \int_{0}^{2} e^{u} \cdot 4 d u

= 100 \cdot \int_{0}^{2} e^{u} \cdot 4 d u

Take the constant out:

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

= 100 \cdot 4 \cdot \int_{0}^{2} e^{u} d u

Use the common integral:

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

= 100 \cdot 4 [e^{u}]_{0}^{2}

Simplify

= 400 [e^{u}]_{0}^{2}

Compute the boundaries:

e^{2} - 1

= 400 (e^{2} - 1)

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What is the integral from 0 to 8 of 100e^{(1/4 x)} ?
The integral from 0 to 8 of 100e^{(1/4 x)} is 400(e^2-1)