Let T Be the Transformation Given by X = 2u $T ^ { - 1 }$

question 194

Essay

Let T be the transformation given by x = 2u + v, y = 3u.(a) A region S in the uv-plane is given below. Sketch the image R of S in the xy-plane. (b) Find the inverse transformation $T ^ { - 1 }$ .(c) Evaluate the double integral $\iint _ { R } e ^ { y / ( 3 x - 2 y ) } d A$ .