Homework Help: Help with an integral please

1. Mar 5, 2012

stonecoldgen

1. The problem statement, all variables and given/known data
This is one of these AP free response questions divided into a,b,c,d,etc. but im just going to ask for a small part of the problem.

I need to integrate y=7tecost

3. The attempt at a solution

I tried using U substitution but it didn't work. I tried things like the following:

Integrate with respect to t (dt).

make ecost=u and t=-cosln(t)

but it seems I am complicating my life. Any tips?

2. Mar 5, 2012

LCKurtz

I would feel very safe telling you there is no elementary antiderivative for that function. My best guess would be it was supposed to be$$\int (7\sin t) e^{\cos t}\, dt$$which would be straightforward.

3. Mar 5, 2012

stonecoldgen

Yeah, I researched a bit around and for some reason this can only be done with a calculator (definite integral).

Wonder how the computer/calculator does it actually.

This was from the 2010 AP Calculus AB test

4. Mar 5, 2012

LCKurtz

Well, your original post did not give a definite integral. That opens the door to numerical routines such as Trapezoidal or Simpson's rules.