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limpfisch

Member

Registered: 2012-05-08

Posts: 11

question to do with double integrals over rectangles

Let R1 denote the rectangle [0, 5] × [–4, 4], R2 the rectangle [0, 5] × [0, 4], and R3 the
rectangle [–5, 0] × [–4, 0]. Suppose that ∫∫R2 f (x, y)dA = 10 , that ∫∫R3 f (x, y)dA = 24
and that f (−x, y) = − f (x, y) for all (x, y). Evaluate ∫∫R1 f (x, y)dA

really not sure on the approach here.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: question to do with double integrals over rectangles

hi limpfisch,

You can make use of the following:

and

I found that it just comes down to adding the two numbers.

EDIT: Oh yes; and I substituted -x for x at one point.

Bob

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