What is the integral from 0 to 1 of e^{x/2} ?

The integral from 0 to 1 of e^{x/2} is 2(sqrt(e)-1)

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integral from 0 to 1 of e^{x/2}

\int_{0}^{1} e^{\frac{x}{2}} d x

2 (e - 1)

Decimal

1.29744 \dots

Solution steps

\int_{0}^{1} e^{\frac{x}{2}} d x

Apply u-substitution

: \int_{0}^{\frac{1}{2}} e^{u} \cdot 2 d u

= \int_{0}^{\frac{1}{2}} e^{u} \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int_{0}^{\frac{1}{2}} e^{u} d u

Use the common integral:

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

= 2 [e^{u}]_{0}^{\frac{1}{2}}

Compute the boundaries:

e - 1

= 2 (e - 1)

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