- #1

- 479

- 4

Where G is the region bounded by x=1, y=x, y=0, z=0, z=2.

How do I evaluate it.

Please help.

- Thread starter squenshl
- Start date

- #1

- 479

- 4

Where G is the region bounded by x=1, y=x, y=0, z=0, z=2.

How do I evaluate it.

Please help.

- #2

daniel_i_l

Gold Member

- 867

- 0

Do you know how to change triple integrals into single-variable integrals?

The general idea is to first evaluate the integral while pretending that 2 of the variables are constant. Then you use that result to integrate over the other variables.

In this case it might be easiest to first evaluate the integral in the triangle 0<=x<=1 and

0<=y<=x while assuming that z is constant. Then integrate that result with z as a variable from 0 to 2. The triangle can be evaluated in a similar way. In other words:

[tex]I = \int^{2}_{0}(\int^{1}_{0}(\int^{1-x}_{0} xyz dy)dx)dz[/tex]

- #3

- 479

- 4

Cheers. I got an answer of 1/3

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