Integrating y=7tecost: Tips and Tricks for Solving AP Free Response Problems

[stonecoldgen]

Homework Statement

This is one of these AP free response questions divided into a,b,c,d,etc. but I am just going to ask for a small part of the problem.

I need to integrate y=7te^cost

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 e^cost=u and t=-cosln(t)



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

 

[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.

 

[stonecoldgen]

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.

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

 

[LCKurtz]

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

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