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  • Similar expressions

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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 933           
 ---           
  50           
  /            
 |             
 |      2      
 |    -x       
 |    ----     
 |     2       
 |   e         
 |  -------- dx
 |    ______   
 |  \/ 2*pi    
 |             
/              
0
$$\int\limits_{0}^{\frac{933}{50}} \frac{e^{\frac{\left(-1\right) x^{2}}{2}}}{\sqrt{2 \pi}}\, dx$$ 
Integral(exp((-x^2)/2)/sqrt(2*pi), (x, 0, 933/50))
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                             ___      /    ___\
 |   -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] 
   /      ___\
   |933*\/ 2 |
erf|---------|
   \   100   /
--------------
      2
$$\frac{\operatorname{erf}{\left(\frac{933 \sqrt{2}}{100} \right)}}{2}$$ 
=
= 
   /      ___\
   |933*\/ 2 |
erf|---------|
   \   100   /
--------------
      2
$$\frac{\operatorname{erf}{\left(\frac{933 \sqrt{2}}{100} \right)}}{2}$$ 
erf(933*sqrt(2)/100)/2
Numerical answer [src] 
0.5
0.5

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

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