Ok so i'm tired of drawing curve and it takes too much time to draw , is there any way to find the area without drawing ? (for both curve with loop and without)
None of my teacher have teached me how to do it without drawing so it make me wonder whether if it is possible . Random guessing only sometimes work.
Lets take an example , area inside $r1=1+cos(\theta)$ and outside $r2=cos(6\theta)$
How can i know if the curve have loop or not , and if it does how can i determine the lower limit and upper limit for the/each integral ?