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Identical expressions
two 000e^(-x^2/ twenty)
2000e to the power of ( minus x squared divide by 20)
two 000e to the power of ( minus x squared divide by twenty)
2000e(-x2/20)
2000e-x2/20
2000e^(-x²/20)
2000e to the power of (-x to the power of 2/20)
2000e^-x^2/20
2000e^(-x^2 divide by 20)
2000e^(-x^2/20)dx
Similar expressions
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)

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

The solution

You have entered [src]

  8              
  /              
 |               
 |          2    
 |        -x     
 |        ----   
 |         20    
 |  2000*E     dx
 |               
/                
0

$$\int\limits_{0}^{8} 2000 e^{\frac{\left(-1\right) x^{2}}{20}}\, dx$$

Integral(2000*E^((-x^2)/20), (x, 0, 8))

Detail solution

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

$\int 2000 e^{\frac{\left(-1\right) x^{2}}{20}}\, dx = 2000 \int e^{\frac{\left(-1\right) x^{2}}{20}}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}$
So, the result is: $2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}$
Add the constant of integration:

$2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}+ \mathrm{constant}$

The answer is:

$2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                  
 |                                                   
 |         2                                         
 |       -x                                          
 |       ----                               /    ___\
 |        20                  ___   ____    |x*\/ 5 |
 | 2000*E     dx = C + 2000*\/ 5 *\/ pi *erf|-------|
 |                                          \   10  /
/

$$\int 2000 e^{\frac{\left(-1\right) x^{2}}{20}}\, dx = C + 2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{\sqrt{5} x}{10} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                     /    ___\
       ___   ____    |4*\/ 5 |
2000*\/ 5 *\/ pi *erf|-------|
                     \   5   /

$$2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{4 \sqrt{5}}{5} \right)}$$

                     /    ___\
       ___   ____    |4*\/ 5 |
2000*\/ 5 *\/ pi *erf|-------|
                     \   5   /

$$2000 \sqrt{5} \sqrt{\pi} \operatorname{erf}{\left(\frac{4 \sqrt{5}}{5} \right)}$$

2000*sqrt(5)*sqrt(pi)*erf(4*sqrt(5)/5)

Numerical answer [src]

7836.1953245522

7836.1953245522

The graph

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

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What you mean?

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

Limits of integration:

The graph:

Piecewise:

The solution