Need help integrating attached pullback please = 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

Name: Need help integrating attached pullback please = x2, y = 2x2 and x = 1
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Description: Need help integrating attached pullback please = 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

Let R be the region bounded by y = x2 and y = 2x2 and x = 1.

Answered: = x2, y = 2x2 and x = 1. Evaluate 3)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Need help integrating attached pullback please

= 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

Expert Solution

Step 1

Let R be the region bounded by y = x² and y = 2x² and x = 1.

Now, 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

Step 2

We know that

SS 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.

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