Use the given transformation to evaluate the integral. (x ? 10y) da, r where r is the triangular region with vertices (0, 0), (9, 1), and (1, 9). x = 9u + v, y = u + 9v

The given change of coordinates has Jacobian

so the area element is

The new region is a right triangle with vertices (0, 0), (1, 0), and (0, 1) in the plane.

Then the integral becomes

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

greater than one

step-by-step explanation: