What is the single iterated integral of a continuous function f over the following region.

Question

The region bounded by the triangle with vertices (0,0),(30,0), and (15, 3).

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∫ ∫ f(x,y) ___

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Answer 1

I[0,3]I[5y,30-5y] f(x,y) dx dy

Note how, when y = 0, x ranges from 0 to 30, and when y = 3, x = 15. This gives us our three vertices.