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Asked Dec 8, 2019
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Problem 10
Use the change of variable technique to evaluate the integral
T. (x² + y² Xx² – y² } dxdy
where R is the region bounded by the graphs of x = 0, x = 1, y =0, y =1 by
R
= 2xy and v= x² - y².
means of the change of variables u =
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Problem 10 Use the change of variable technique to evaluate the integral T. (x² + y² Xx² – y² } dxdy where R is the region bounded by the graphs of x = 0, x = 1, y =0, y =1 by R = 2xy and v= x² - y². means of the change of variables u =

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Step 1

Given integral and region R are,

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|(* +y° )(x² - y²) dxdy, where R is the region bounded by the graphs x = 0, x = 1, y = 0 and y = 1

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Step 2

Given the values of u and v as,

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=(x`- y*) 2xy and v =

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Step 3

Now, changing the v...

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dudv Where, J is jacobi. dxdy ôu ôu ây J = since,u = 2xy and v = ôx ây 2y 2x -2y 2.x -4y - 4x = -4(x + y²) dudv= (x + y* ) dxdy = - dudv 4 Then dxdy = 4(x* + y²) ||

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