Question

Determine whether the statement is true or false. If it is false, explain why or give an example. If f(x, y) ≤ g(x, y) for all (x, y) in R, and both f and g are continuous over R, then ∫_R∫ f(x, y) dA ≤ ∫_R∫ g(x, y) dA.

Solution

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Answered 12 months ago
Answered 12 months ago
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At every point (x,y)(x, y) in the region RR the function f(x,y)f(x, y) has a lower value than g(x,y)g(x, y) so integrating f(x,y)f(x,y) over the region will yield a lower value than integrating g(x,y)g(x, y).

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