Mister Exam

Other calculators

Integral of exp(-2ax^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

  1. Now simplify:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
                                      _____     /      ___\
  /                    ___   ____    / -1       |a*x*\/ 2 |
 |                   \/ 2 *\/ pi *  /  --- *erfi|---------|
 |        2                       \/    a       |    ____ |
 |  -2*a*x                                      \  \/ -a  /
 | e        dx = C - --------------------------------------
 |                                     4                   
/                                                          
$${{\sqrt{\pi}\,\mathrm{erf}\left(\sqrt{2}\,\sqrt{a}\,x\right)}\over{ 2^{{{3}\over{2}}}\,\sqrt{a}}}$$
The answer [src]
/  ___   ____    /  ___   ___\                                  
|\/ 2 *\/ pi *erf\\/ 2 *\/ a /                                  
|-----------------------------  for And(a > -oo, a < oo, a != 0)
<               ___                                             
|           4*\/ a                                              
|                                                               
\              1                           otherwise            
$${{\sqrt{\pi}\,\mathrm{erf}\left(\sqrt{2}\,\sqrt{a}\right)}\over{2^{ {{3}\over{2}}}\,\sqrt{a}}}$$
=
=
/  ___   ____    /  ___   ___\                                  
|\/ 2 *\/ pi *erf\\/ 2 *\/ a /                                  
|-----------------------------  for And(a > -oo, a < oo, a != 0)
<               ___                                             
|           4*\/ a                                              
|                                                               
\              1                           otherwise            
$$\begin{cases} \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}{\left(\sqrt{2} \sqrt{a} \right)}}{4 \sqrt{a}} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\1 & \text{otherwise} \end{cases}$$

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