Change of Variables in Multiple Integrals

Multiple integrals are often used to evaluate areas, volumes, mass distributions, and other physical quantities over regions in two or three dimensions. In many problems, however, the original region may have complicated curved boundaries when expressed in Cartesian coordinates. These complex boundaries can make the limits of integration difficu...

In multivariable calculus, evaluating a multiple integral over a region, R, often seems difficult as the region, R, may have complex boundaries in x and y coordinates.

To simplify this mathematical evaluation, a change of variables is made into a new coordinate system defined by the variables u and v