Mister Exam

Integral of e^(-2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1         
  /         
 |          
 |   -2*x   
 |  E     dx
 |          
/           
0           
$$\int\limits_{0}^{1} e^{- 2 x}\, dx$$
Integral(E^(-2*x), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

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

      1. The integral of the exponential function is itself.

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                    
 |                 -2*x
 |  -2*x          e    
 | E     dx = C - -----
 |                  2  
/                      
$$\int e^{- 2 x}\, dx = C - \frac{e^{- 2 x}}{2}$$
The graph
The answer [src]
     -2
1   e  
- - ---
2    2 
$$\frac{1}{2} - \frac{1}{2 e^{2}}$$
=
=
     -2
1   e  
- - ---
2    2 
$$\frac{1}{2} - \frac{1}{2 e^{2}}$$
1/2 - exp(-2)/2
Numerical answer [src]
0.432332358381694
0.432332358381694
The graph
Integral of e^(-2x) dx

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