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

The integral from-2 to 3 of e^{x/2} is 2(e^{3/2}-1/e)

integral from-2 to 3 of e^{x/2}

\int_{- 2}^{3} e^{\frac{x}{2}} d x

2 (e^{\frac{3}{2}} - \frac{1}{e})

Decimal

8.22761 \dots

Solution steps

\int_{- 2}^{3} e^{\frac{x}{2}} d x

Apply u-substitution

= \int_{- 1}^{\frac{3}{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_{- 1}^{\frac{3}{2}} e^{u} d u

Use the common integral:

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

= 2 [e^{u}]_{- 1}^{\frac{3}{2}}

Compute the boundaries:

e^{\frac{3}{2}} - \frac{1}{e}

= 2 (e^{\frac{3}{2}} - \frac{1}{e})

\int_{0}^{1} x ln (1 + x) d x

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\int_{1}^{e} \frac{( ln ( x ) ) ^{4}}{x} d x

\int_{1}^{e} (x^{2} - 2 x + 3) ln (x) d x

What is the integral from-2 to 3 of e^{x/2} ?
The integral from-2 to 3 of e^{x/2} is 2(e^{3/2}-1/e)