8.(10 points) Evaluate the imegralf 1svyd where R is the region bounded by the curves 2 u xy-1,xy.-3, yu-2, andy-6 using the transformation questions (a) Sketch and shade the region R in the xy-plane. y , by answering the following x -, óu (b) Transform all the boundary curves and sketch the transformed region in the uv-plane. (c) Transform the given integral in terms of u and v (don't forget the Jacobian). (d) Evaluate that integrl (e) Why was this transformation so helpful for the integral we were given? 8.(10 points) Evaluate the imegralf 1svyd where R is the region bounded by the curves 2 u xy-1,xy.-3, yu-2, andy-6 using the transformation questions (a) Sketch and shade the region R in the xy-plane. y , by answering the following x -, óu (b) Transform all the boundary curves and sketch the transformed region in the uv-plane. (c) Transform the given integral in terms of u and v (don't forget the Jacobian). (d) Evaluate that integrl (e) Why was this transformation so helpful for the integral we were given?


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