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Solving integrals/ exp(-x)*sin(x)^2

Integral of exp(-x)*sin(x)^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |   -x    2      
 |  e  *sin (x) dx
 |                
/                 
0
$$\int\limits_{0}^{1} e^{- x} \sin^{2}{\left(x \right)}\, dx$$ 
Integral(exp(-x)*sin(x)^2, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                        
 |                           2     -x        2     -x             -x       
 |  -x    2             3*sin (x)*e     2*cos (x)*e     2*cos(x)*e  *sin(x)
 | e  *sin (x) dx = C - ------------- - ------------- - -------------------
 |                            5               5                  5         
/
$$\int e^{- x} \sin^{2}{\left(x \right)}\, dx = C - \frac{3 e^{- x} \sin^{2}{\left(x \right)}}{5} - \frac{2 e^{- x} \sin{\left(x \right)} \cos{\left(x \right)}}{5} - \frac{2 e^{- x} \cos^{2}{\left(x \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         2     -1        2     -1             -1       
2   3*sin (1)*e     2*cos (1)*e     2*cos(1)*e  *sin(1)
- - ------------- - ------------- - -------------------
5         5               5                  5
$$- \frac{3 \sin^{2}{\left(1 \right)}}{5 e} - \frac{2 \sin{\left(1 \right)} \cos{\left(1 \right)}}{5 e} - \frac{2 \cos^{2}{\left(1 \right)}}{5 e} + \frac{2}{5}$$ 
=
= 
         2     -1        2     -1             -1       
2   3*sin (1)*e     2*cos (1)*e     2*cos(1)*e  *sin(1)
- - ------------- - ------------- - -------------------
5         5               5                  5
$$- \frac{3 \sin^{2}{\left(1 \right)}}{5 e} - \frac{2 \sin{\left(1 \right)} \cos{\left(1 \right)}}{5 e} - \frac{2 \cos^{2}{\left(1 \right)}}{5 e} + \frac{2}{5}$$ 
2/5 - 3*sin(1)^2*exp(-1)/5 - 2*cos(1)^2*exp(-1)/5 - 2*cos(1)*exp(-1)*sin(1)/5
Numerical answer [src] 
0.133848726999004
0.133848726999004

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

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