ImageShack® - Online Photo and Video Hosting
Not sure how to find the limits and how to start, thanks..
ImageShack® - Online Photo and Video Hosting
Not sure how to find the limits and how to start, thanks..
I would recommend you start by drawing a picture. You should see that x+ y+ z= 1, which can also be written z= 1- x- y, is a plane that forms a triangle in the first quadrant ($\displaystyle x\ge 0$, $\displaystyle y\ge 0$, $\displaystyle z\ge 0$) with vertices at (1, 0, 0), (0, 1, 0), (0, 0, 1). If you choose to integrate in the order "dzdydx" then note that the projection of that plane down to the xy-plane is the triangle with vertices at (1, 0), (0, 1), and (0, 0) (the projections of (1, 0, 0), (0, 1, 0), and (0, 0, 1) respectively). The line (0, 1) to (1, 0) is x+ y= 1, which is the same as y= 1- x, and that, in turn, projects to the x- axis as segment between x= 0 and x= 1. That is, to integrate over that region, x will have to go from 0 to 1. For each x, y will have to go from 0 up to 1- x. [b]For each (x, y), z will have to go from 0 to 1- x- y.
Integrate using those limits of integration.
[ math ] is working again!