Question

Asked Nov 18, 2019

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can u help me with pullbacks and integration plz

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Step 1

Given that the integral,

Step 2

here, *R* is the parallelogram with vertices at (-1, -2), (3, 0), (2, 2), and (-2, 0).

Equation of line through the point (-1, -2), (3, 0) is

*x* - 2*y* = 3

Equation of line through the point (3, 0), (2, 2) is

2*x* + *y* = 6

Equation of line through the point (2, 2), (-2, 0) is

*x* - 2*y* = - 2

Equation of line through the point (-2, 0), (-1, -2) is

2*x *+ *y *= - 4

Assume that,

*x* - 2*y *= *u*

and

2*x *+ *y *=* v*

Then, *u* = 3 and *u* = - 2

*v* = 6 and *v* = - 4

Also, *x* - 2*y *= *u*

2*x *+ *y *=* v*

This implies that,

Step 3

Use the pullback (method of change of variable), for this find the value of Jacobian ...

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