I dont know how to change it to cylindrical coordinates and set up the integral for it.
First draw a picture. Set up an xy- coordinate system. Since x ranges between x= 0 and x= 3, draw vertical lines there. Now, for each x, y ranges between and . But squaring either of those gives or , the circle with center at (0,0) and radius 3. The right half of that circle lies between x= 0 and x= 3.
That is, the region you are integrating is a semi-circle, the portion of in the x> 0 half-plane.
Of course, and .
That gives the integral yeKciM gives.
(Except that I would use "r" rather than " ". I reserve " " for spherical coordinates.)
and looks like this when drown
yes, you are correct but it's (for me at least) much easier to remember (or don't forget) when using like this
Polar coordinates :
natural limits for polar coordinates :
Cylindrical coordinates :
natural limits for cylindrical coordinates :
Spherical coordinates :
natural limits for spherical coordinates:
P.S. @ larryboi7 : when changing the limits u must always know that they can't be greater than the natural limits , but can be smaller ... let's say for spherical goes from to , and never can go to let's say from to but can from to just for example
and if not by any condition in your task limits of are changed u'll use natural limits for those
and what is more important (if u don't realize it) when for ur integral changing limits for it's obvious that limits are from to 3, because u have circle with center in (0,0) so ur limits goes from zero to radius of ur circle, but if ur circle is shifted (doesn't have center in point (0,0) ) then u must do a little calculating to see how do your changes...