MAT 211 Lecture 7: Lecture_7

■EXAMPLE 6 Use the Change of Variables Formula to calculate e4_ydzdy, where P is the parallelogram spanned by the vectors (4, 1), (3, 3) in Figure 10. 7,4) (3,3) a. Solution Step I. Define a map. We can convert our double integral to an integral over the unit square R = [0, 1] x [0,1] if we can find a map that sends R to P.The following linear map does the job: G(u, u) = (4" + 30, " + 3v) Indeed, G (1, o) (4, 1) and G (0, l)-(33), so it maps R to P because linear maps map parallelograms to parallelograms.