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

Integral of exp((-x^2)/2) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |     2    
 |   -x     
 |   ----   
 |    2     
 |  e     dx
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0
∫01e(−1)x22 dx\int\limits_{0}^{1} e^{\frac{\left(-1\right) x^{2}}{2}}\, dx 
Integral(exp((-x^2)/2), (x, 0, 1))
Detail solution

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

  1. Add the constant of integration:

    2πerf⁡(2x2)2+constant\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}+ \mathrm{constant}

The answer is:

2πerf⁡(2x2)2+constant\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{2} x}{2} \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                        
 |                                         
 |    2                           /    ___\
 |  -x              ___   ____    |x*\/ 2 |
 |  ----          \/ 2 *\/ pi *erf|-------|
 |   2                            \   2   /
 | e     dx = C + -------------------------
 |                            2            
/
∫e(−1)x22 dx=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}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
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 exp((-x^2)/2) dx

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

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