Will the real TeeEm please stand up!

one question I made and added earlier

one question I made and added earlier

Quick question. How come the sides of he rectangle are 4a and a respectively? Surely you can only relate them like this if this information is given in the question?

clearly ! did this in a hurry and forgot to add this bit of information in the text.

sorry

Any good method for this?
(please attach I do not have home-works any more!!!)

I have the correct answer (which is part of an undergrad question to which I am writing a solution)
It is just that the method seems a bit to long and I do not want to rewrite the solution as this integral lies somewhere in the middle of a longish problem

Thanks

Any good method for this?
(please attach I do not have home-works any more!!!)

I have the correct answer (which is part of an undergrad question to which I am writing a solution)
It is just that the method seems a bit to long and I do not want to rewrite the solution as this integral lies somewhere in the middle of a longish problem

Thanks

Can it be done using A level methods? Im thinking hyperbolic.


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What is the answer? I did...something, but it's weird

it is a mess to type

take the limit of the answer as k tends to zero

you should get 2pi

Got pi first but just forgot to account for chain rule on the arctan
Separating into two logs and then using IVP on both is fairly quick no? I guess It's not very pretty. And it's assuming the derivative of arctan is expected knowledge

I've got some cool integral questions somewhere, I hope @TeeEm won't mind if I post one or two here occasionally?

Here's some of the easiest:

$\int \sqrt{tan x}\ dx$

$\int arctan( \sqrt{x} )\ dx$

No problem

the first one is famous

the second not sure .... is it hard without limits?