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FP2 Polar coordinates

Hi would like some help as i am not getting the right answer in the FP2 June 2010.Here is my workings in short june 2010 Fp2.PNG.This is what the mark scheme has to say:ms.PNG
Thanks,
Smith
Original post by smith50
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The limits on your integral are incorrect. What do you get at the points of intersection of the two curves?

You will find it helpful, I think, to draw on the two areas you are subtracting to get the desired result.
Reply 2
Original post by ghostwalker
The limits on your integral are incorrect. What do you get at the points of intersection of the two curves?

You will find it helpful, I think, to draw on the two areas you are subtracting to get the desired result.



Yes the denominators of the limits should be 18 - but how do you do the next step?
My two coordinates of intersection was (2,pi/18) and (2,5pi/18).

I am really stuck on the next part of the area

smith
Reply 3
Are you confused about the part of the mark scheme that you circled? That's just the integral from whatever to whatever of 2r^2 dt evaluated...
Well the area is:

12π185π18(1.5+sin3θ)222  dθ\displaystyle\frac{1}{2}\int^{ \frac{5\pi}{18}}_{\frac{\pi}{18}}(1.5+\sin 3\theta)^2-2^2\;\mathrm{d\theta}

And if you split it into two integrals, you end up with the final term they have.

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