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3*exp(-2*x)

Integral of 3*exp(-2*x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |     -2*x   
 |  3*e     dx
 |            
/             
0             
$$\int\limits_{0}^{1} 3 e^{- 2 x}\, dx$$
Integral(3*exp(-2*x), (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    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:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                        
 |                     -2*x
 |    -2*x          3*e    
 | 3*e     dx = C - -------
 |                     2   
/                          
$$\int 3 e^{- 2 x}\, dx = C - \frac{3 e^{- 2 x}}{2}$$
The graph
The answer [src]
       -2
3   3*e  
- - -----
2     2  
$$\frac{3}{2} - \frac{3}{2 e^{2}}$$
=
=
       -2
3   3*e  
- - -----
2     2  
$$\frac{3}{2} - \frac{3}{2 e^{2}}$$
3/2 - 3*exp(-2)/2
Numerical answer [src]
1.29699707514508
1.29699707514508
The graph
Integral of 3*exp(-2*x) dx

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