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2000e^(-x^2/20)
Solving integrals/ 2000e^(-x^2/20)

You entered:

2000e^(-x^2/20)

What you mean?

2000*e^((-x^2)/20)
 
2000*e^(-x^(1/10))
 
2000*e^((-x^2)/20)
 
2000*e^(2*(-x)/20)
 
2000*e^((-x^2)/20)
 
2000*e^((-x^2)/20)

Integral of 2000e^(-x^2/20) dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  8              
  /              
 |               
 |          2    
 |        -x     
 |        ----   
 |         20    
 |  2000*E     dx
 |               
/                
0
∫082000e(−1)x220 dx\int\limits_{0}^{8} 2000 e^{\frac{\left(-1\right) x^{2}}{20}}\, dx 
Integral(2000*E^((-x^2)/20), (x, 0, 8))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫2000e(−1)x220 dx=2000∫e(−1)x220 dx\int 2000 e^{\frac{\left(-1\right) x^{2}}{20}}\, dx = 2000 \int e^{\frac{\left(-1\right) x^{2}}{20}}\, dx

    1. Don't know the steps in finding this integral.

      But the integral is

      5πerf⁡(5x10)\sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}

    So, the result is: 20005πerf⁡(5x10)2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}

  2. Add the constant of integration:

    20005πerf⁡(5x10)+constant2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}+ \mathrm{constant}

The answer is:

20005πerf⁡(5x10)+constant2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                                  
 |                                                   
 |         2                                         
 |       -x                                          
 |       ----                               /    ___\
 |        20                  ___   ____    |x*\/ 5 |
 | 2000*E     dx = C + 2000*\/ 5 *\/ pi *erf|-------|
 |                                          \   10  /
/
∫2000e(−1)x220 dx=C+20005πerf⁡(5x10)\int 2000 e^{\frac{\left(-1\right) x^{2}}{20}}\, dx = C + 2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}
Simplify
The graph
0.08.01.02.03.04.05.06.07.0010000
Plot the graph f(x)
The answer [src] 
                     /    ___\
       ___   ____    |4*\/ 5 |
2000*\/ 5 *\/ pi *erf|-------|
                     \   5   /
20005πerf⁡(455)2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{4 \sqrt{5}}{5} \right)} 
=
= 
                     /    ___\
       ___   ____    |4*\/ 5 |
2000*\/ 5 *\/ pi *erf|-------|
                     \   5   /
20005πerf⁡(455)2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{4 \sqrt{5}}{5} \right)} 
2000*sqrt(5)*sqrt(pi)*erf(4*sqrt(5)/5)
Numerical answer [src] 
7836.1953245522
7836.1953245522
The graph
Integral of 2000e^(-x^2/20) dx

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

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