1 / | | -x /x\ | e *sin|-| dx | \2/ | / 0
Integral(sin(x/2)/E^x, (x, 0, 1))
Use integration by parts, noting that the integrand eventually repeats itself.
For the integrand :
Let and let .
Then .
For the integrand :
Let and let .
Then .
Notice that the integrand has repeated itself, so move it to one side:
Therefore,
Now simplify:
Add the constant of integration:
The answer is:
/ -x /x\ /x\ -x | 4*e *sin|-| 2*cos|-|*e | -x /x\ \2/ \2/ | e *sin|-| dx = C - ------------ - ------------ | \2/ 5 5 | /
-1 -1 2 4*e *sin(1/2) 2*cos(1/2)*e - - -------------- - -------------- 5 5 5
=
-1 -1 2 4*e *sin(1/2) 2*cos(1/2)*e - - -------------- - -------------- 5 5 5
Use the examples entering the upper and lower limits of integration.