I encountered the following question online:
Evaluate $$ \iint_D \frac{x^3}{x^2 + y^2} dA$$ where D is the region $$D := {(x − 1)^2 + y^2 ≤ 1} ∩ {y ≥ 0}$$
Could you begin by stating your approach and how to deal with similar problems in the future. This seems so fundamental but I haven't dealt with this problem type yet.
Also, note an application this problem type has and an intuition as to how one would come to construct this problem. Please elucidate sufficiently for those new to this domain.