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