i tried to use Latex but i failed so here's the problem the double integral of (x^2 + y^2) ^1/2 dx dy the inner limit is from 0 to (3y-y^2)^1/2 and the outer limit is from 0 to 3
i know how to change the coordinates but having problem figuring out the limits for this problem
Okay, correcting for that:
leads to or so . That is the same as , a circle with center at (0, 3/2) and radius 3/2. The original function, then, is the right semicircle.
So when you said "changing the coordinates" you did NOT mean "reverse the order of integration" but rather "change to polar coordinates"!
To stay on the right side of the y-axis, take from to and, of course, r from 0 to 3/2. The "differential of area" in polar coordinates is so your integral becomes .
That should be easy!