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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

2 (e - 1)

Decimal Notation

3.43656 \dots

Solution steps

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

Apply u-substitution

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

= \int_{0}^{1} 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}^{1} e^{u} d u

Use the common integral:

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

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

Compute the boundaries:

e - 1

= 2 (e - 1)

\frac{d y}{d x} = \frac{x y ^{3}}{1 + x ^{2}}

\int 4 - 4 x d x

\frac{d y}{y} - 4 x d x = 0

f (x) = x ln (x)

x^{3}, x^{2} + x, - 1, 1.5

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