double integral question
Ok. I have a quick question about the limits of integration for a problem:
*I am going to use @ for theta.*
Integrate f(x,y) = x + y over the region R bounded by r = cos(@)
I converted the function to a polar function and got r cos(@) + r sin(@) and a r dr d@ making it:
r^2[cos(@) + sin(@)]dr d@
now for the limits of integration I am using 0 to cos(@) and 0 to 2 pi Is this correct or should I use 0 to 1 for the dr since cos can only go from 0 to 1? I am thinking I am correct with my first method but I just wanted to check. Also if I made any other mistakes feel free to point those out as well.
Originally Posted by billbarber
is the same as the circle ...
so are you saying it would be easier to just convert the bound r = cos(@) to rectangular coordinates?
or are you saying that the theta goes from 0 to pi and the r goes from 0 to 1/2?