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(e^(-x))*(sin(x/2))

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |   -x    /x\   
 |  e  *sin|-| dx
 |         \2/   
 |               
/                
0                
$$\int\limits_{0}^{1} e^{- x} \sin{\left(\frac{x}{2} \right)}\, dx$$
Integral(sin(x/2)/E^x, (x, 0, 1))
Detail solution
  1. Use integration by parts, noting that the integrand eventually repeats itself.

    1. For the integrand :

      Let and let .

      Then .

    2. For the integrand :

      Let and let .

      Then .

    3. Notice that the integrand has repeated itself, so move it to one side:

      Therefore,

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                       -x    /x\        /x\  -x
 |                     4*e  *sin|-|   2*cos|-|*e  
 |  -x    /x\                   \2/        \2/    
 | e  *sin|-| dx = C - ------------ - ------------
 |        \2/               5              5      
 |                                                
/                                                 
$${{2\,\left(-2\,\sin \left({{x}\over{2}}\right)-\cos \left({{x }\over{2}}\right)\right)\,e^ {- x }}\over{5}}$$
The graph
The answer [src]
       -1                        -1
2   4*e  *sin(1/2)   2*cos(1/2)*e  
- - -------------- - --------------
5         5                5       
$${{2}\over{5}}-{{e^ {- 1 }\,\left(4\,\sin \left({{1}\over{2}}\right) +2\,\cos \left({{1}\over{2}}\right)\right)}\over{5}}$$
=
=
       -1                        -1
2   4*e  *sin(1/2)   2*cos(1/2)*e  
- - -------------- - --------------
5         5                5       
$$- \frac{4 \sin{\left(\frac{1}{2} \right)}}{5 e} - \frac{2 \cos{\left(\frac{1}{2} \right)}}{5 e} + \frac{2}{5}$$
Numerical answer [src]
0.129765527639961
0.129765527639961
The graph
Integral of (e^(-x))*(sin(x/2)) dx

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