Mister Exam

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Identical expressions
e^- zero . two *x
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Similar expressions
e^+0.02*x

Integral of e^-0.02*x dx

The solution

You have entered [src]

  1         
  /         
 |          
 |    x     
 |  ----- dx
 |  50___   
 |  \/ E    
 |          
/           
0

$$\int\limits_{0}^{1} \frac{x}{e^{\frac{1}{50}}}\, dx$$

Integral(x/E^(1/50), (x, 0, 1))

Detail solution

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

$\int \frac{x}{e^{\frac{1}{50}}}\, dx = \frac{\int x\, dx}{e^{\frac{1}{50}}}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
So, the result is: $\frac{x^{2}}{2 e^{\frac{1}{50}}}$
Add the constant of integration:

$\frac{x^{2}}{2 e^{\frac{1}{50}}}+ \mathrm{constant}$

The answer is:

$\frac{x^{2}}{2 e^{\frac{1}{50}}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                 2  -1/50
 |   x            x *e     
 | ----- dx = C + ---------
 | 50___              2    
 | \/ E                    
 |                         
/

$$\int \frac{x}{e^{\frac{1}{50}}}\, dx = C + \frac{x^{2}}{2 e^{\frac{1}{50}}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

 -1/50
e     
------
  2

$$\frac{1}{2 e^{\frac{1}{50}}}$$

 -1/50
e     
------
  2

$$\frac{1}{2 e^{\frac{1}{50}}}$$

exp(-1/50)/2

Numerical answer [src]

0.490099336653378

0.490099336653378

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

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Identical expressions

Similar expressions

Integral of e^-0.02*x dx

Limits of integration:

The graph:

Piecewise:

The solution