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Triple Integration for Volume

  • Thread starter aaronfue
  • Start date
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1. Homework Statement

Find the volume of the solid in the first octant bounded by the graphs of:
z=1-y2
y=2x
x=3

2. Homework Equations

I was able to graph all three but I can't picture the region for integration. I'm not sure if I even have to graph it or if I can get my limits without the graph.

3. The Attempt at a Solution
 
Last edited:

haruspex

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Please post an attempt at writing out the integral.
 
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After graphing the equations, I came up with:

[itex]\int^{1}_{-1}[/itex] [itex]\int^{3}_{0}[/itex] [itex]\int^{1}_{0}[/itex] dzdxdy (this order was given as a hint)

My final answer was 6?
 

haruspex

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No, you need to put the given constraints as bounds in the integrals. The order needed also results from the dependencies in those bounds. The y bounds depend on x, and the z bounds depend on y, and therefore on x too. So the order should be z, y, x.
 

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