The question is to find the area of a disk, r ≤ 2a×cos(θ) as in the figure "example-just an illustration" I used two methods, each gave different wrong answers - integrate 2a×cos(θ) dθ dr - from θ=0 to θ=π/2 and from r=2a to r=2a×cos(θ) ; then I simply multiplied the answer by 2. - integrate 2a×cos(θ) dθ dr - from θ=0 to θ=2π and from r=2a to r=2a×cos(θ) I was hopping to get the right answer using the first method, but surprisingly it didn't work, integration seems to be fine I even used wolfram to check it. ----------------- I have another small question. I had a question about finding the volume of flipped cone "its point in the origin and its shape is in the positive side of z-axis", its height is the same as its base radius so that, r=h z=h, thus r=z "example-just an illustration" http://01.edu-cdn.com/files/static/mcgrawhillprof/9780071624756/INVERTED_CONE_WATER_TANK_PROBLEM_01.GIF [Broken] thing is, when I put the limits say : r=0 ⇒ h //// z=0 ⇒ r //// θ=0 ⇒ 2π . It give wrong answer but r=0 ⇒ z //// z=0 ⇒ h //// θ=0 ⇒ 2π . give the right one that's really confusing!!