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Solving integrals/ e^(-2x)cosx

Integral of e^(-2x)cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |   -2*x          
 |  E    *cos(x) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} e^{- 2 x} \cos{\left(x \right)}\, dx$$ 
Integral(E^(-2*x)*cos(x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                   
 |                                 -2*x    -2*x       
 |  -2*x                 2*cos(x)*e       e    *sin(x)
 | E    *cos(x) dx = C - -------------- + ------------
 |                             5               5      
/
$$\int e^{- 2 x} \cos{\left(x \right)}\, dx = C + \frac{e^{- 2 x} \sin{\left(x \right)}}{5} - \frac{2 e^{- 2 x} \cos{\left(x \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
              -2    -2       
2   2*cos(1)*e     e  *sin(1)
- - ------------ + ----------
5        5             5
$$- \frac{2 \cos{\left(1 \right)}}{5 e^{2}} + \frac{\sin{\left(1 \right)}}{5 e^{2}} + \frac{2}{5}$$ 
=
= 
              -2    -2       
2   2*cos(1)*e     e  *sin(1)
- - ------------ + ----------
5        5             5
$$- \frac{2 \cos{\left(1 \right)}}{5 e^{2}} + \frac{\sin{\left(1 \right)}}{5 e^{2}} + \frac{2}{5}$$ 
2/5 - 2*cos(1)*exp(-2)/5 + exp(-2)*sin(1)/5
Numerical answer [src] 
0.39352735657365
0.39352735657365

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

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