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  • Identical expressions

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  • Similar expressions

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Solving integrals/ 200/(sqrt(2pi)3,3)exp(-((x-0,3)^2)/22)

Integral of 200/(sqrt(2pi)3,3)exp(-((x-0,3)^2)/22) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 -11                                 
 ----                                
  10                                 
   /                                 
  |                                  
  |                             2    
  |                  -(x - 3/10)     
  |                  -------------   
  |        200             22        
  |   -------------*e              dx
  |   /  ______   \                  
  |   |\/ 2*pi *33|                  
  |   |-----------|                  
  |   \     10    /                  
  |                                  
 /                                   
-12/5
$$\int\limits_{- \frac{12}{5}}^{- \frac{11}{10}} \frac{200}{\frac{33}{10} \sqrt{2 \pi}} e^{\frac{\left(-1\right) \left(x - \frac{3}{10}\right)^{2}}{22}}\, dx$$ 
Integral((200/((sqrt(2*pi)*33/10)))*exp((-(x - 3/10)^2)/22), (x, -12/5, -11/10))
Detail solution

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

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

      But the integral is

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                                                         
 |                                                                                          
 |                           2                                                              
 |                -(x - 3/10)                                                               
 |                -------------                                 ___     /  ____            \
 |      200             22                     ____   ____  5*\/ 2      |\/ 22 *(-3/10 + x)|
 | -------------*e              dx = C + 100*\/ 22 *\/ pi *---------*erf|------------------|
 | /  ______   \                                                ____    \        22        /
 | |\/ 2*pi *33|                                           33*\/ pi                         
 | |-----------|                                                                            
 | \     10    /                                                                            
 |                                                                                          
/
$$\int \frac{200}{\frac{33}{10} \sqrt{2 \pi}} e^{\frac{\left(-1\right) \left(x - \frac{3}{10}\right)^{2}}{22}}\, dx = C + 100 \sqrt{22} \sqrt{\pi} \frac{5 \sqrt{2}}{33 \sqrt{\pi}} \operatorname{erf}{\left(\frac{\sqrt{22} \left(x - \frac{3}{10}\right)}{22} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                 /     ____\                  /    ____\
         ____    |27*\/ 22 |          ____    |7*\/ 22 |
  1000*\/ 11 *erf|---------|   1000*\/ 11 *erf|--------|
                 \   220   /                  \  110   /
- -------------------------- + -------------------------
              33                           33
$$- \frac{1000 \sqrt{11} \operatorname{erf}{\left(\frac{27 \sqrt{22}}{220} \right)}}{33} + \frac{1000 \sqrt{11} \operatorname{erf}{\left(\frac{7 \sqrt{22}}{110} \right)}}{33}$$ 
=
= 
                 /     ____\                  /    ____\
         ____    |27*\/ 22 |          ____    |7*\/ 22 |
  1000*\/ 11 *erf|---------|   1000*\/ 11 *erf|--------|
                 \   220   /                  \  110   /
- -------------------------- + -------------------------
              33                           33
$$- \frac{1000 \sqrt{11} \operatorname{erf}{\left(\frac{27 \sqrt{22}}{220} \right)}}{33} + \frac{1000 \sqrt{11} \operatorname{erf}{\left(\frac{7 \sqrt{22}}{110} \right)}}{33}$$ 
-1000*sqrt(11)*erf(27*sqrt(22)/220)/33 + 1000*sqrt(11)*erf(7*sqrt(22)/110)/33
Numerical answer [src] 
25.8638114105778
25.8638114105778

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

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