Let R be the region in R2 bounded by the lines y= 221, and y =...

 

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Let R be the region in R2 bounded by the lines y= 22²1, and y = 0. Consider the substitution g: R² i. Compute g'(x, y) and det (g'(x, y)). ii. Determine g(R) and give a sketch of the region in (u, v)-coordinates. Show complete working out for full marks. (Hint: Use the approach covered in class) iii. Compute R² given by g(x, y) = (x², 2y) = (u, v). J₁² r sin(y) dr dy by using the substitution g. R Let R be the region in R2 bounded by the lines y= 22²1, and y = 0. Consider the substitution g: R² i. Compute g'(x, y) and det (g'(x, y)). ii. Determine g(R) and give a sketch of the region in (u, v)-coordinates. Show complete working out for full marks. (Hint: Use the approach covered in class) iii. Compute R² given by g(x, y) = (x², 2y) = (u, v). J₁² r sin(y) dr dy by using the substitution g. R