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PhysicsWow

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**Summary::**Calculate a double integral via appropriate change of variables in R^2

Suppose I have f(x,y)=sqrt(y^12 + 1). I need to integrate y from (x)^(1/11) to 1 and x from 0 to 1. The inner integral is in y and outer in x. How do I calculate integration(f(x,y)dxdy) ?

My Approach: I know that I have to change the variables to u-v plane from x,y, and I have seen the boundaries of the required region. But I can't express x and y as a function in (u,v)? Can someone give an insight into what should u and v appropriately be? Also, could you explain a bit why they should be assumed so?