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  • Similar expressions

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

Integral of 1/(sqrt(2pi))*e^(-x^2/2) 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
$$\int\limits_{0}^{1} \frac{e^{\frac{\left(-1\right) x^{2}}{2}}}{\sqrt{2 \pi}}\, dx$$ 
Integral(E^((-x^2)/2)/sqrt(2*pi), (x, 0, 1))
Detail solution

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

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                    
 |                                                     
 |     2                             ___      /    ___\
 |   -x                ___   ____  \/ 2       |x*\/ 2 |
 |   ----            \/ 2 *\/ pi *--------*erf|-------|
 |    2                               ____    \   2   /
 |  E                             2*\/ pi              
 | -------- dx = C + ----------------------------------
 |   ______                          2                 
 | \/ 2*pi                                             
 |                                                     
/
$$\int \frac{e^{\frac{\left(-1\right) x^{2}}{2}}}{\sqrt{2 \pi}}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \frac{\sqrt{2}}{2 \sqrt{\pi}} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   /  ___\
   |\/ 2 |
erf|-----|
   \  2  /
----------
    2
$$\frac{\operatorname{erf}{\left(\frac{\sqrt{2}}{2} \right)}}{2}$$ 
=
= 
   /  ___\
   |\/ 2 |
erf|-----|
   \  2  /
----------
    2
$$\frac{\operatorname{erf}{\left(\frac{\sqrt{2}}{2} \right)}}{2}$$ 
erf(sqrt(2)/2)/2
Numerical answer [src] 
0.341344746068543
0.341344746068543

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

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