Let T be the transformation given by x = 2u + v, y = u + 2v.(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 $\iint _ { R } ( - x + 2 y ) ^ { 2 } \cos ( 2 x - y ) d A$ .

Question

Let T be the transformation given by x = 2u + v, y = u + 2v.(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 $\iint _ { R } ( - x + 2 y ) ^ { 2 } \cos ( 2 x - y ) d A$ .

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The Answer of Let T be the transformation given by x = 2u + v, y = u + 2v.(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 $\iint _ { R } ( - x + 2 y ) ^ { 2 } \cos ( 2 x - y ) d A$ .

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

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