set up integral for volume between cylinders and planes

[spdrmncoo]

Can you help me, please?

Set up the integral for the volume between the cylinders y = 5 - x^2, y = 4x^2, and the planes z = 0 and x + z = 1

I already did the following:

. . .\(\displaystyle \L \int\, \int_{-1}^1\, \int_0^{1-x}\, dz\, dx\, dy\)
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Edited by stapel -- Reason for edit: fixing formatting

 

[galactus]

Set up the integral for the volume between the cylinders \(\displaystyle y = 5 - x^{2},\;\ y = 4x^{2}\), and the planes \(\displaystyle z = 0\) and \(\displaystyle x + z = 1\)

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Here's a set up(I believe). Try rearranging the variables of integration and see if you get the same thing.

\(\displaystyle \L\\\int_{-1}^{1}\int_{0}^{1-x}\int_{4x^{2}}^{5-x^{2}}dydzdx\)