Calculus II: Integration over polar curves

[@MathforThought]

In example 5, the first curve is r=5(1-sin(theta)) not r=5(1-cos(theta))

[@teodorlepki1549]

you have a very soothing voice

[@IDareYou93]

Thank You!..

[@anjj21k]

how did u get the shape to be that way for example #2? isnt it flipped upside down on the diagram

[@MathforThought]

But it's not.

[@AdityaTutika]

(i) how to know if we have to draw cardioid facing up or facing down.
(ii) in example 5 why is it drawn facing down even if a/b=1

[@MathforThought]

I usually plot a few points to get a general shape.
For example 5, sure I could have drawn it the other way, but the area won't change in any case so...

[@jasonmantri2658]

in example 2, could we also find the negative angle of 7pi/6 and integrate with 11pi/6 as an alternative?

[@MathforThought]

No. The direction won't be right then.