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exp(-(z^2)/2)
Solving integrals/ exp(-(z^2)/2)

Integral of exp(-(z^2)/2) dz

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2         
  /         
 |          
 |     2    
 |   -z     
 |   ----   
 |    2     
 |  e     dz
 |          
/           
0
$$\int\limits_{0}^{2} e^{\frac{\left(-1\right) z^{2}}{2}}\, dz$$ 
Integral(exp(-z^2/2), (z, 0, 2))
Detail solution

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

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                        
 |                                         
 |    2                           /    ___\
 |  -z              ___   ____    |z*\/ 2 |
 |  ----          \/ 2 *\/ pi *erf|-------|
 |   2                            \   2   /
 | e     dz = C + -------------------------
 |                            2            
/
$$\int e^{\frac{\left(-1\right) z^{2}}{2}}\, dz = C + \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} z}{2} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___   ____    /  ___\
\/ 2 *\/ pi *erf\\/ 2 /
-----------------------
           2
$$\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\sqrt{2} \right)}}{2}$$ 
=
= 
  ___   ____    /  ___\
\/ 2 *\/ pi *erf\\/ 2 /
-----------------------
           2
$$\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\sqrt{2} \right)}}{2}$$
Упростить
Numerical answer [src] 
1.19628801332261
1.19628801332261
The graph
Integral of exp(-(z^2)/2) dz

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

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