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December 5th, 2015, 09:59 PM   #1
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Question about Multiple Integration

Can someone here solve this? I am desperate, I made an account just for this. I have solved parts one and two of this problem, but c and d are driving me insane:

c) f,g are real valued functions on a subset, A, of R^n. Show that if the integral of f and g over A exist, then the integral of fg over A exists.

d) Again, f has the same conditions as before, but let B be a subset of A. Show that if the integral of f exists and B has volume, then the integral of f over B exists.

Help on either would be incredible!

Volume refers to Jordan measure and integration is Riemann type.

Last edited by skipjack; December 6th, 2015 at 12:25 AM.
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December 6th, 2015, 05:16 PM   #2
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Off the top of my head for (c) you can squeeze any Riemann sum for fg between one for min(f)min(g) and max(f)max(g).

For (d) I'd look at the function g = f on B and 0 on A\B.

You still have to do all the details but that's how I'd get started.
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