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  • Integral of (1/sqrt(2*pi))*exp((-x^2)/2)
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  • (1/sqrt(2*pi))*exp((-x^2)/2)dx

  • Similar expressions

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Solving integrals/ (1/sqrt(2*pi))*exp((-x^2)/2)

Integral of (1/sqrt(2*pi))*exp((-x^2)/2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  x                    
  /                    
 |                     
 |                2    
 |              -x     
 |              ----   
 |       1       2     
 |  1*--------*e     dx
 |      ______         
 |    \/ 2*pi          
 |                     
/                      
0
$$\int\limits_{0}^{x} 1 \cdot \frac{1}{\sqrt{2 \pi}} e^{\frac{\left(-1\right) x^{2}}{2}}\, dx$$
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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                            
 |                                           ___      /    ___\
 |               2             ___   ____  \/ 2       |x*\/ 2 |
 |             -x            \/ 2 *\/ pi *--------*erf|-------|
 |             ----                           ____    \   2   /
 |      1       2                         2*\/ pi              
 | 1*--------*e     dx = C + ----------------------------------
 |     ______                                2                 
 |   \/ 2*pi                                                   
 |                                                             
/
$${{\sqrt{\pi}\,\mathrm{erf}\left({{x}\over{\sqrt{2}}}\right)}\over{2 \,\sqrt{\pi}}}$$
Simplify
The answer [src] 
   /    ___\
   |x*\/ 2 |
erf|-------|
   \   2   /
------------
     2
$$\frac{\operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$$ 
=
= 
   /    ___\
   |x*\/ 2 |
erf|-------|
   \   2   /
------------
     2
$$\frac{\operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$$
Simplify

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

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