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e^((-x^2)/2)

Integral of 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
 |          
/           
0           
01e(1)x22dx\int\limits_{0}^{1} e^{\frac{\left(-1\right) x^{2}}{2}}\, dx
Integral(E^((-x^2)/2), (x, 0, 1))
The answer (Indefinite) [src]
  /                                        
 |                                         
 |    2                           /    ___\
 |  -x              ___   ____    |x*\/ 2 |
 |  ----          \/ 2 *\/ pi *erf|-------|
 |   2                            \   2   /
 | E     dx = C + -------------------------
 |                            2            
/                                          
e(1)x22dx=C+2πerf(2x2)2\int e^{\frac{\left(-1\right) x^{2}}{2}}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
The answer [src]
                /  ___\
  ___   ____    |\/ 2 |
\/ 2 *\/ pi *erf|-----|
                \  2  /
-----------------------
           2           
2πerf(22)2\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2}}{2} \right)}}{2}
=
=
                /  ___\
  ___   ____    |\/ 2 |
\/ 2 *\/ pi *erf|-----|
                \  2  /
-----------------------
           2           
2πerf(22)2\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2}}{2} \right)}}{2}
sqrt(2)*sqrt(pi)*erf(sqrt(2)/2)/2
Numerical answer [src]
0.855624391892149
0.855624391892149
The graph
Integral of e^((-x^2)/2) dx

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