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exp(-(x^2)/2)/2/pi

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  • Similar expressions

  • exp((x^2)/2)/2/pi
Solving integrals/ exp(-(x^2)/2)/2/pi

Integral of exp(-(x^2)/2)/2/pi dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |     2    
 |   -x     
 |   ----   
 |    2     
 |  e       
 |  ----- dx
 |   2*pi   
 |          
/           
0
$$\int\limits_{0}^{1} \frac{e^{\frac{\left(-1\right) x^{2}}{2}}}{2 \pi}\, dx$$
Simplify
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

      ErfRule(a=-1/2, b=0, c=0, context=exp(-x**2/2), symbol=x)

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                 
 |                                  
 |    2                             
 |  -x                     /    ___\
 |  ----            ___    |x*\/ 2 |
 |   2            \/ 2 *erf|-------|
 | e                       \   2   /
 | ----- dx = C + ------------------
 |  2*pi                   ____     
 |                     4*\/ pi      
/
$${{\sqrt{\pi}\,\mathrm{erf}\left({{x}\over{\sqrt{2}}}\right)}\over{2 ^{{{3}\over{2}}}\,\pi}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         /  ___\
  ___    |\/ 2 |
\/ 2 *erf|-----|
         \  2  /
----------------
        ____    
    4*\/ pi
$${{\sqrt{\pi}\,\mathrm{erf}\left({{1}\over{\sqrt{2}}}\right)}\over{2 ^{{{3}\over{2}}}\,\pi}}$$ 
=
= 
         /  ___\
  ___    |\/ 2 |
\/ 2 *erf|-----|
         \  2  /
----------------
        ____    
    4*\/ pi
$$\frac{\sqrt{2} \operatorname{erf}{\left(\frac{\sqrt{2}}{2} \right)}}{4 \sqrt{\pi}}$$
Simplify
Numerical answer [src] 
0.136176851399633
0.136176851399633
The graph
Integral of exp(-(x^2)/2)/2/pi dx

    Use the examples entering the upper and lower limits of integration.

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