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

The integral from 1 to 3 of e^{-(x^2)/2} is 0.39430…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int_{1}^{3} e^{- \frac{x ^{2}}{2}} d x

0.39430 \dots

Solution steps

\int_{1}^{3} e^{- \frac{x ^{2}}{2}} d x

Apply exponent rule:

\frac{a ^{n}}{b ^{n}} = (\frac{a}{b})^{n}

\frac{x ^{2}}{2} = (\frac{x}{2})^{2}

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the nonelementary integral:

\int e^{- u^{2}} d u = \frac{π}{2} erf (u)

= 2 [\frac{π}{2} erf (u)]_{\frac{1}{2}}^{\frac{3}{2}}

Compute the boundaries:

0.27881 \dots

= 2 \cdot 0.27881 \dots

Simplify

= 0.39430 \dots

\int_{4}^{7} \frac{x}{x - 3} d x

\int_{0}^{8} 11000 e^{- 0.019 t} d t

\int_{0}^{5} \frac{1}{x + 1} d x

\int_{0}^{3} (5 x - 9) d x

\int_{0}^{4} 1 + x^{\frac{1}{2}} d x

What is the integral from 1 to 3 of e^{-(x^2)/2} ?
The integral from 1 to 3 of e^{-(x^2)/2} is 0.39430…