Mister Exam

Other calculators

e^(-x)sin(2x)
Solving integrals/ e^(-x)sin(2x)

Integral of e^(-x)sin(2x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |   -x            
 |  E  *sin(2*x) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} e^{- x} \sin{\left(2 x \right)}\, dx$$ 
Integral(E^(-x)*sin(2*x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                   
 |                                   -x    -x         
 |  -x                   2*cos(2*x)*e     e  *sin(2*x)
 | E  *sin(2*x) dx = C - -------------- - ------------
 |                             5               5      
/
$$\int e^{- x} \sin{\left(2 x \right)}\, dx = C - \frac{e^{- x} \sin{\left(2 x \right)}}{5} - \frac{2 e^{- x} \cos{\left(2 x \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
              -1    -1       
2   2*cos(2)*e     e  *sin(2)
- - ------------ - ----------
5        5             5
$$- \frac{\sin{\left(2 \right)}}{5 e} - \frac{2 \cos{\left(2 \right)}}{5 e} + \frac{2}{5}$$ 
=
= 
              -1    -1       
2   2*cos(2)*e     e  *sin(2)
- - ------------ - ----------
5        5             5
$$- \frac{\sin{\left(2 \right)}}{5 e} - \frac{2 \cos{\left(2 \right)}}{5 e} + \frac{2}{5}$$ 
2/5 - 2*cos(2)*exp(-1)/5 - exp(-1)*sin(2)/5
Numerical answer [src] 
0.394334380421838
0.394334380421838
The graph
Integral of e^(-x)sin(2x) dx

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

    © Mister Exam – Calculator