2012-03-28, 04:21 PM
Just a note that for the first qns you were looking at the diagram centred at x = 1, in which your integral would have made a little more sense if you instead transformed the graph to the left by 1 unit. It is a common mistake to forget that the origin for polar should still be at the same origin as the cartesian axes, so be more careful next time. You should do the transformation trick occasionally to exploit symmetries in integrals (and more obvious trigo integrals), but do be careful when doing that.
Polar coordinates are supposed to make things easier, because you can pull all kinds of trigo tricks here and there, and lots of shortcuts too. Makes life a lot easier if you're not dealing with flat stuff. Also sometimes used for DEs, and heavily needed for Quantum. Anything touching e^(_), be prepared to pull some trigo... <---- those will kill me one day too.
As a note, please always label your integrals i.e. y=0, sqrt(2x - x^2). The pendantic annoyance is little compared to the strands of hair you pull out in frustration trying to debug your working.
Hadriel
Polar coordinates are supposed to make things easier, because you can pull all kinds of trigo tricks here and there, and lots of shortcuts too. Makes life a lot easier if you're not dealing with flat stuff. Also sometimes used for DEs, and heavily needed for Quantum. Anything touching e^(_), be prepared to pull some trigo... <---- those will kill me one day too.
As a note, please always label your integrals i.e. y=0, sqrt(2x - x^2). The pendantic annoyance is little compared to the strands of hair you pull out in frustration trying to debug your working.
Hadriel