Ok I figured out what to do, but this last algebra is bugging me.
= 2 * [(e - e) - (-1/e - 1/e)]
= 4/e
does it simplify to 0 (+2/e +2/e)
which equals 4/e?
∫ sin(2t)*e^[cos(t)] dt (from t=0 to π)
My work:
trig identity: sin2t= 2sintcost
bring constant to the outside
=> 2 ∫ sin(t)cos(t)*e^[cos(t)] dt (from t=0 to π)
I did u substitution and did
u=cos(t)
du=-sin(t)dt
new intervals:
cos(pi)=-1
cos(0)=1
Im not sure what to after this. Do I divide du=-sint(dt) by negative 1 and bring that -1 to the outside of integral since there is only a sin(t)dt not -sin(t)dt?
I appreciate any help!
Hello, Steelers72!
I couldn't follow what you did, but you got the right answer.
I'll drop the limits for now . . .
We have: .
By parts: .
Then: .
. . . . .
. . . . .
. . . . .
Evaluate: .
. . . . . . .
. . . . . . .
. . . . . . .