Thread: Where have I gone wrong here? (Area enclosed by polar coords)

Hi guys,

I'm asked to show that the area enclosed by the curve



where

is 16/3

I proceeded as follows



after some working I arrived at





as required.

I was then asked to show that the initial line divides the area enclosed by the curve in the ratio 1:7. I thought this would simply be a case of putting in pi/2 and zero into the above integral and obtaining 2/3 (thus the other part would be 14/3 - a ratio of 1:7) but instead I got -1/3!

So I tried putting in 0 and -pi/2 into the formula and I got 17/3.

These two sum to give the required whole area but do not split the area into 1:7. I have absolutely no idea where to go from here.

Any help would be much appreciated

MUst be simple arithmetic since we get

2[ sin(t)+1/2cos(2t)+1/3sin^3(t)] (0 to pi/2)=

2[(1 -1/2 +1/3) -1/2]= 2/3

Originally Posted by Calculus26

MUst be simple arithmetic since we get

2[ sin(t)+1/2cos(2t)+1/3sin^3(t)] (0 to pi/2)=

2[(1 -1/2 +1/3) -1/2]= 2/3

...

*facepalm*

thanks