Double integral, switching to polar coordinates

**dankelly07** · April 25th 2009, 02:41 PM

$ \iint_{\text{R}} {{\text{exp( - x}}^{\text{2}} {\text{ - y}}^{\text{2}} {\text{)dxdy}}} $

,where R is the quadrant x>0, y>0

$ \iint_{\text{R}} {{\text{exp( - (x}}^{\text{2}} {\text{ + y}}^{\text{2}} {\text{))dxdy}}} $

$ \iint_{} {{\text{exp( - r}}^{\text{2}} {\text{)rdrd}}\theta } $ ]

Ok so I've done a couple of these now, but I always seem to have the problem of picturing this geometrically. Can anyone explain a simple way of knowing how equations like these will look on a graph?

what does it mean 'where R is in the quadrant, x> 0, y>0 ??

I always have problems when trying to define the limits for these types of integrals..

**Chris L T521** · April 25th 2009, 03:08 PM

Originally Posted by dankelly07

$ \iint_{\text{R}} {{\text{exp( - x}}^{\text{2}} {\text{ - y}}^{\text{2}} {\text{)dxdy}}} $

,where R is the quadrant x>0, y>0

$ \iint_{\text{R}} {{\text{exp( - (x}}^{\text{2}} {\text{ + y}}^{\text{2}} {\text{))dxdy}}} $

$ \iint_{} {{\text{exp( - r}}^{\text{2}} {\text{)rdrd}}\theta } $ ]

Ok so I've done a couple of these now, but I always seem to have the problem of picturing this geometrically. Can anyone explain a simple way of knowing how equations like these will look on a graph?

what does it mean 'where R is in the quadrant, x> 0, y>0 ??

I always have problems when trying to define the limits for these types of integrals..

The restrictions $x>0,y>0$ imply that you're looking at the first quadrant. In terms of polar coordinates, you're considering a region with radius starting from the pole, and it goes to infinity. Theta goes from 0 to $\frac{\pi}{2}$ . So you want to consider evaluating the integral $\int_0^{\frac{\pi}{2}}\int_0^{\infty}e^{-r^2}r\,dr\,d\theta$

Thread: Double integral, switching to polar coordinates

LinkBack

Thread Tools

Display

Double integral, switching to polar coordinates

Similar Math Help Forum Discussions

Double Integral with Polar Coordinates

Double integral in polar coordinates

double integral using polar coordinates

Double integral in polar coordinates 2

Double integral in polar coordinates

Search Tags