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Topic: [ap-calculus] Re: Integral Problem - Finney DeMana #59, p. 575
Replies: 1   Last Post: Apr 5, 2005 9:52 AM

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Richard J Maher

Posts: 80
Registered: 12/6/04
[ap-calculus] Re: Integral Problem - Finney DeMana #59, p. 575
Posted: Apr 5, 2005 9:52 AM
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Hello George,

The answers are the same, since they differ by a constant. Remember

(1/2)tan^2 u = (1/2)sec^2 u - 1/2.

Hope this helps.

Dick Maher



Richard J. Maher
Mathematics and Statistics
Loyola University Chicago
6525 N. Sheridan Rd.
Chicago, Illinois 60626
1-773-508-3565
rjm@math.luc.edu



On Mon, 4 Apr 2005, George Becker wrote:

This problem asks for the integral of sin(x-3)/cos^3(x-3)dx. Using
substitution with u=cosx yields 1/(2cos^2(x-3))+ C which is the answer
the book provides. Alternatively, this could be written as 1/2(sec^2(x-3)).

Question is when you change the original integral to
tan(x-3)sec^2(x-3)dx
and then integrate by substitution with u=tanx, you get 1/2(tan^2(x-3))+ C
which does not appear to be the same answer, even using common trig
identities.

Why does these two answers not agree?

George Becker
Pope John HS
Sparta, NJ


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