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I have to integrate some function $f(x, y, z)$ over the región $E$ where $E$ is the prism bounded by the planes $z = x$, $x = 2$, $y = 4$ and the coordinate planes ($x = 0$, $y = 0$ and $z = 0$). I say $E = \{ (x, y, z): 0 \leq x \leq 2, 0 \leq y \leq 4, 0 \leq z \leq x\},$ but I integrate over this region and my result differs from the one given in the book. Since I know the integral is well calculated, the only place that can be wrong is my interpretation of $E.$ Can somebody tell me how describe $E$ properly?

Chris Suarez
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1 Answers1

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Your description of $ E $ appears correct. Either you set up the integral incorrectly, you evaluated it incorrectly, you didn't realize why your answer was equivalent to the book's, or the book is wrong. If you give more details maybe we could help you figure out which.

Mark S.
  • 23,925