To practice integration I am doing Princeton University integration exams and this question came up...I used a method on it which I am not sure is valid...if it isn't please explain why not, and if they're is an easier method please do tell
Let
THen
so we get
Partial fractions reveals
integrating we get
Now back substituting we get
So is that right?
back-substituting is not an efficient method of solving these problems. You should also change the limits of the integral as well.
so the substitution will change
to
as when
and when .
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Here is another question that examiners/universities love to ask on this topic.
Could you explain the following error in my working.
I wish to solve the integral
Using the substitution
the limits stay the same because at
so the integral becomes
so
therefore
however so the integral cannot be equal to zero.
So where did I go wrong?
P.S. the question is for Mathstud28 no other takers please.
Bobak
The integral is easy, it's an obvious arctangent. Now, why am I sayin' this, 'cause you can "see" it. First, take and contemplate its derivative, which is and the conclusion follows quickly.
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I suggest you to find nice integrals, like hard ones. (Of course, when sayin' "hard" I mean "it looks hard but with a simple trick we can kill it.")
Not sure what you mean here.
everything is transparent, could you expand on the significant of his discontinuity ?There is a diguised infinite discontinuity at t=0
Bobak
Do you have any examples of these?
is a standard form, among with many others, Krizalid is calling the integral easy because if you spot the standard form (and are good with the chain rule) there is actually nothing to do, but i assume the test was intended for student that may not be familiar with it.
Contact me directly if you want some resources.
Bobak