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

Question 89

Essay

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. 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 . (b) Find the inverse transformation T−1T ^ { - 1 } .(c) Evaluate the double integral ∬R(−x+2y)2cos⁡(2x−y)dA\iint _ { R } ( - x + 2 y ) ^ { 2 } \cos ( 2 x - y ) d A .

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