1 / | | -x | e *cos(x)*1 dx | / 0
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 e *sin(x) cos(x)*e | e *cos(x)*1 dx = C + ---------- - ---------- | 2 2 /
-1 -1 1 e *sin(1) cos(1)*e - + ---------- - ---------- 2 2 2
=
-1 -1 1 e *sin(1) cos(1)*e - + ---------- - ---------- 2 2 2
Use the examples entering the upper and lower limits of integration.