# = x2, y = 2x2 and x = 1. Evaluate3) Let R be the region bounded by yxy2 dxdyVu, yv and first pulling the integral back to an integral in u, v spaceby setting x

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Need help integrating attached pullback please help_outlineImage Transcriptionclose= x2, y = 2x2 and x = 1. Evaluate 3) Let R be the region bounded by y xy2 dxdy Vu, y v and first pulling the integral back to an integral in u, v space by setting x fullscreen
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Step 1

Let R be the region bounded by y = x2 and y = 2x2 and x = 1. help_outlineImage TranscriptioncloseNow, we need to evaluate ff xy2 dx dy by setting x the integral back to an integral in u, v space. Vu, y v and first pilling fullscreen
Step 2

We know th... help_outlineImage TranscriptioncloseSS f(x, y) dx I g (u, v) J du dv, where J is the Jacobian Jacobian is defined as, |дх дх ди J ду ду дu av Also, y x2v = u, y 2x2 ->v - 2u and x 1> vu = 1 => u = 1. And for v u, v = 2u => u = 0 So, overall we got, v = u, v = 2u, u = 1 and u = 0. Thus, the integral in step-1 becomes (z" Vu v2/ du dv , where J is the Jacobian. fullscreen

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