In finding the area in Polar Coordinates...Why does the lower limit which was -pi/4 turns into 0?
See below...

Find the area enclosed by one loop of the four-leaved rose r=cos2theta

I want to find what will make cos2theta equal 0, right? And that will be pi/2 and 3pi/2 but I will have to divide by 2 which will turn theta into pi/4 and 3pi/4.

Question

In finding the area in Polar Coordinates...Why does the lower limit which was -pi/4 turns into 0?
See below...

Find the area enclosed by one loop of the four-leaved rose r=cos2theta

I want to find what will make cos2theta equal 0, right? And that will be pi/2 and 3pi/2 but I will have to divide by 2 which will turn theta into pi/4 and 3pi/4.

anonymous · Answer

I know how to solve this problem, I just do not know why 0 is now the lower limit!

anonymous · Answer

because of symmetry, you can find the area of half the petal going starting from 0

anonymous · Answer

Is it because it is a loop and that it must return back to 0?

anonymous · Answer

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anonymous · Answer

Are you shading half of a whole loop?

anonymous · Answer

Thanks ..I think I get it!