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Find the image of the set

`S`

under the given transformation a)

`S`

is the square bounded by the lines

`u=0,u=1,v=0,v=1;x=v,y=u(1+v^(2))`

b)

`S`

is the triangular region with vertices

`(0,0),(1,1),(0,1);,x=u^(2),y=v`

.