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

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Homework Help Overview

The discussion revolves around the integration of the function y=7tecost, which is part of an AP free response question. Participants are exploring the challenges associated with finding an antiderivative for this function.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts integration using u-substitution but finds it complicated. Some participants suggest that there may not be an elementary antiderivative for the function and propose an alternative integral involving e^{\cos t}. Others question the nature of the integral, noting that it may require numerical methods for evaluation.

Discussion Status

The discussion is active, with participants sharing insights about the integration problem and exploring different interpretations of the original question. There is acknowledgment that numerical methods might be necessary for evaluation, particularly in the context of the AP exam.

Contextual Notes

Participants note that the original post did not specify a definite integral, which influences the methods available for solving the problem. The problem is also contextualized as being from the 2010 AP Calculus AB test.

stonecoldgen
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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=7tecost






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?
 
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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.
 
LCKurtz said:
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
 
stonecoldgen said:
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.
 

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