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Integrating to find an area of a region.

Decide whether to integrate with respect to "X" and "Y", then find the area of the region. x+y^2=42, x+y=0.

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Please see the attached file.

While standard method is to write y as a function of x and just integrate
in this case if we go ...

Solution Summary

The solution shows in addition to the answer also why one integration route is better than the other.