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
I'm asked to show that the area enclosed by the curve
I proceeded as follows
after some working I arrived at
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