If I'm asked to find the volume of a solid that lies below the surface z = f(x,y), and above to region in the xy-plane bounded by a certain curve...and I'm only given 3 limits of integration, what do I do?(adsbygoogle = window.adsbygoogle || []).push({});

For example:

z = 9 - x - y

Given y = 0, x = 3, y = (2x)/3

At first I thought I could get another limit for my x integral by solving y = (2x)/3 for x -- however, I then end up with an answer that has an x or a y in it. So I figure this must be wrong.

I then chose the limits for my x integral to be 0 and 3, (I choose 0 randomly) and I got an answer of 18. The books answer was 19. So I believe I am close.

Is that how I find the last limit if I am only given 3?

Thank you!

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# Homework Help: Choosing the limits of integration

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