Volume enclosed between $x=3y^2+z^2$ and $x=7$.

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Find the volume enclosed between the paraboloid $x=3y^2+z^2$ and the plane $x=7$.

I've tried cartesian but have struggled with the limits, is it possible to do this with polar coordinates?

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I have given the solution in a hand written image and hopefully it is clear and legible Good Luck

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