blyatman
Well-Known Member
Yes, please see one of the subsequent posts.These are all beyond the scope of the syllabus.
Yes, please see one of the subsequent posts.These are all beyond the scope of the syllabus.
My method is similar to yours. DI table may make the integration by parts neater.I have a feeling this is not the fastest method...
(the proof is left as an exercise to the reader.)
From here, I will use the result , which is not difficult to verify via the appropriate double angle identity.
Note that the absolute value is important when evaluating the lower bound.
Have anyone figured out?This one is challenging if you can't think of a useful substitution.
This integral itself should be quite routine. Getting the final answer in terms of pi is slightly tricky.This one is relatively routine.
intuition said it was φ-like but i didn't want to stay up that late to figure it out;Clearly, the useful substitution is
As it turns out, the indefinite counterparts of some of these integrals have no closed-form solutions (I tried googling a solution to no.9), so some of these definite integrals must be solved (assuming they can be solved conventionally) without directly integrating into the anti-derivative, similar to how the integral of exp(x)cos(x) is done by using integration by parts twice (so that we have 2*integral = something).
These are Mr Blyatman's question. Ill work them up later today
How are you supposed to know phi is a good sub here? I mean looking at the original question aloneHave anyone figured out?
The trick is:
Clearly, the useful substitution is
Inspection.How are you supposed to know phi is a good sub here? I mean looking at the original question alone
After dividing top and bottom by 27^x, the integral is in the form 1/(p^x+q^x+r^x). If this integral has an elementary form, then there must be a relationship between p,q and r. After some trial and error, you would get that relationship.How are you supposed to know phi is a good sub here? I mean looking at the original question alone
Has anyone attempted this?This one is tedious.
That... doesn't necessarily have to be true, but my intuition agrees with that.If this integral has an elementary form, then there must be a relationship between p,q and r. After some trial and error, you would get that relationship.
No attempt for 2 weeksFeel free to share your attempt.
Math is not really my area but I tried nonethelessFeel free to share your attempt.
Math is not really my area but I tried nonetheless
yeah I kinda realized that while going to sleep but I have no idea how to integrate sinx/x. so I kinda just went mehGood try!
Unfortunately, there's a mistake in this piece of integral.
Fortunately, it doesn't affect the final answer.