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

Integral of exp(-x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |     2   
 |   -x    
 |  e    dx
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0
∫01e−x2 dx\int\limits_{0}^{1} e^{- x^{2}}\, dx 
Integral(exp(-x^2), (x, 0, 1))
Detail solution

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

  1. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                           
 |                            
 |    2            ____       
 |  -x           \/ pi *erf(x)
 | e    dx = C + -------------
 |                     2      
/
∫e−x2 dx=C+πerf⁡(x)2\int e^{- x^{2}}\, dx = C + \frac{\sqrt{\pi} \operatorname{erf}{\left(x \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] 
  ____       
\/ pi *erf(1)
-------------
      2
πerf⁡(1)2\frac{\sqrt{\pi} \operatorname{erf}{\left(1 \right)}}{2} 
=
= 
  ____       
\/ pi *erf(1)
-------------
      2
πerf⁡(1)2\frac{\sqrt{\pi} \operatorname{erf}{\left(1 \right)}}{2} 
sqrt(pi)*erf(1)/2
Numerical answer [src] 
0.746824132812427
0.746824132812427
The graph
Integral of exp(-x^2) dx

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

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