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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |   -x          
 |  2  *sin(x) dx
 |               
/                
0
$$\int\limits_{0}^{1} 2^{- x} \sin{\left(x \right)}\, dx$$ 
Integral(2^(-x)*sin(x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                     
 |                                                      
 |  -x                      cos(x)        log(2)*sin(x) 
 | 2  *sin(x) dx = C - --------------- - ---------------
 |                      x    x    2       x    x    2   
/                      2  + 2 *log (2)   2  + 2 *log (2)
$$\int 2^{- x} \sin{\left(x \right)}\, dx = C - \frac{\log{\left(2 \right)} \sin{\left(x \right)}}{2^{x} \log{\left(2 \right)}^{2} + 2^{x}} - \frac{\cos{\left(x \right)}}{2^{x} \log{\left(2 \right)}^{2} + 2^{x}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     1            cos(1)      log(2)*sin(1)
----------- - ------------- - -------------
       2               2               2   
1 + log (2)   2 + 2*log (2)   2 + 2*log (2)
$$- \frac{\log{\left(2 \right)} \sin{\left(1 \right)}}{2 \log{\left(2 \right)}^{2} + 2} - \frac{\cos{\left(1 \right)}}{2 \log{\left(2 \right)}^{2} + 2} + \frac{1}{\log{\left(2 \right)}^{2} + 1}$$ 
=
= 
     1            cos(1)      log(2)*sin(1)
----------- - ------------- - -------------
       2               2               2   
1 + log (2)   2 + 2*log (2)   2 + 2*log (2)
$$- \frac{\log{\left(2 \right)} \sin{\left(1 \right)}}{2 \log{\left(2 \right)}^{2} + 2} - \frac{\cos{\left(1 \right)}}{2 \log{\left(2 \right)}^{2} + 2} + \frac{1}{\log{\left(2 \right)}^{2} + 1}$$ 
1/(1 + log(2)^2) - cos(1)/(2 + 2*log(2)^2) - log(2)*sin(1)/(2 + 2*log(2)^2)
Numerical answer [src] 
0.296002117341662
0.296002117341662

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

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