Question 3 (15 marks, C3) Let O = {(x, y, z) E R³ | z>0}, and let : O→ R³ be the mapping defined as V(x, y, z) = (x,x+y,

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Question 3 15 Marks C3 Let O X Y Z E R Z 0 And Let O R Be The Mapping Defined As V X Y Z X X Y 1 (33.48 KiB) Viewed 18 times

Question 3 (15 marks, C3) Let O = {(x, y, z) E R³ | z>0}, and let : O→ R³ be the mapping defined as V(x, y, z) = (x,x+y, x² + ²). (a) Show that is a smooth change of variables. (b) Let K = {(x, y, z) |0 ≤ x ≤ 4, −x ≤ y ≤ 4 − x, √25 – x² < z ≤ √36 − x² } . (x + y)z Use the change of variables theorem to evaluate the integral x² + 2² dxdydz. [6] [9]