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I have a series of practice questions for Calculus 3 that as me to solve some definite double or triple integrals, and ask me to sketch the area or volume of the integral. I'm not really sure how to do this?

For example, I'm given the following integral and asked to sketch the area:

Integral from 0 to x^2 dy surrounded by integral from 0 to 1 dx.

Or another problem, for example, asks me to sketch the volume:

Integral from 0 to 2 of 3 dy, surrounded by integral from 0 to 1 dx.

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1 Answer 1

The integrals over $y$ do not contain $y$ and so the double integrals are simple area integrals you know from Calc I. For example, the first integral is the area under the parabola $y=x^2$ from $x=0$ to $x=1$. Can you do the second?

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Okay, well the second one would be something like: 3y evaluated from 0 to 2 = 6 for the inner integral, and: 6x evaluated from 0 to 1 = 6 for the outer integral, right? –  PseudoPsyche Mar 5 '13 at 5:08

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