Length of loop

Question

Length of loop

dramaqueen1201 · Answer

the question is as attached

faiqraees · Answer

Question from Kangaroo competition?

dramaqueen1201 · Answer

and my working are attached too
now the answer is supposed to be $$4\sqrt{3}$$ but i got something that's close but not exactly it

dramaqueen1201 · Answer

@FaiqRaees no, sorry

dramaqueen1201 · Answer

i mean, when you put it in decimals, my answer and the right answer are close but it's not really that so i tried to look at my calculations but everything looks fine to me? was my method wrong?

legomyego180 · Answer

Youre using the formula for a polar arclength, but your coordinates are Cartesian arent they?

legomyego180 · Answer

im not sure, thats just a hunch.

dramaqueen1201 · Answer

oh... probably... >.<

ganeshie8 · Answer

Your formula is fine.

ganeshie8 · Answer

Can you explain me below step ? 

|dw:1471114491620:dw|

dramaqueen1201 · Answer

@ganeshie8 OOOOHHHH!! bollocks! i ate away some of the powers, didn't i??? wait let me try and correct that pronto!!!

faiqraees · Answer

She I suppose made an illogical substitution $t=t^2 $

ganeshie8 · Answer

Haha yeah. Looks you should get below as the integrand
$$\sqrt{(t^2+1)^2}$$

dramaqueen1201 · Answer

@ganeshie8 i am so sorry!! it works fine now *facepalm*

ganeshie8 · Answer

That's okay :) Also, you may check your work with wolfram http://www.wolframalpha.com/input/?i=Integrate%5Bsqrt((2t)%5E2+%2B+(1-t%5E2)%5E2),+%7Bt,+-sqrt(3),sqrt(3)%7D%5D