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

Integral of e^(-2x^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |       2   
 |   -2*x    
 |  e      dx
 |           
/            
0
$$\int\limits_{0}^{1} e^{- 2 x^{2}}\, dx$$
Simplify
Detail solution

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

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                         
 |                                          
 |      2            ___   ____    /    ___\
 |  -2*x           \/ 2 *\/ pi *erf\x*\/ 2 /
 | e      dx = C + -------------------------
 |                             4            
/
$${{\sqrt{\pi}\,\mathrm{erf}\left(\sqrt{2}\,x\right)}\over{2^{{{3 }\over{2}}}}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  ___   ____    /  ___\
\/ 2 *\/ pi *erf\\/ 2 /
-----------------------
           4
$${{\sqrt{\pi}\,\mathrm{erf}\left(\sqrt{2}\right)}\over{2^{{{3}\over{ 2}}}}}$$ 
=
= 
  ___   ____    /  ___\
\/ 2 *\/ pi *erf\\/ 2 /
-----------------------
           4
$$\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\sqrt{2} \right)}}{4}$$
Simplify
Numerical answer [src] 
0.598144006661304
0.598144006661304
The graph
Integral of e^(-2x^2) dx

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

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