Q1

Suppose R is a region in the wy-plane, and let S be made from R by reecting in the :EELXiS. Use a change of variables argument to show that R and 5' have the same area. (Hint: write the map from the Qty-plane to the Qtyplane that correSponds to reection.) Of course reection is intuitively area preserving. Here we're giving a formal argument for why that is the case. [2] Suppose T(u,v, w) = (:1:(u,v,w), y(u,v,w), z(u,v, w)) is a transformation of nowspace to atyz-Space. Let R(u,w,v) = T(u,v,w). Suppose we do an integral using T as our change of variables, or we do the same integral using R. Why do we get the same iterated integral in both cases? [1]