What is the integral from 2 to 4 of 1/(e^{0.5x)} ?

The integral from 2 to 4 of 1/(e^{0.5x)} is 0.46508…

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integral from 2 to 4 of 1/(e^{0.5x)}

\int_{2}^{4} \frac{1}{e ^{0.5 x}} d x

0.46508 \dots

Solution steps

\int_{2}^{4} \frac{1}{e ^{0.5 x}} d x

Apply Integration By Parts

: [\frac{x}{e ^{0.5 x}} - \int - 0.5 e^{- 0.5 x} x d x]_{2}^{4}

= [\frac{x}{e ^{0.5 x}} - \int - 0.5 e^{- 0.5 x} x d x]_{2}^{4}

\int - 0.5 e^{- 0.5 x} x d x = - 2 (- 0.5 e^{- 0.5 x} x - e^{- 0.5 x})

= [\frac{x}{e ^{0.5 x}} - (- 2 (- 0.5 e^{- 0.5 x} x - e^{- 0.5 x}))]_{2}^{4}

Simplify

= [\frac{x}{e ^{0.5 x}} + 2 (- 0.5 e^{- 0.5 x} x - e^{- 0.5 x})]_{2}^{4}

Compute the boundaries:

0.46508 \dots

= 0.46508 \dots

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What is the integral from 2 to 4 of 1/(e^{0.5x)} ?
The integral from 2 to 4 of 1/(e^{0.5x)} is 0.46508…