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I am confused about how to find the bounds of integration for the following triple integral. I seem to have trouble figuring out how to parameterize these curves (like the paraboloid, below).

Also, based on my parameterization, the function that I am integrating over (mass density function, $x^2+y^2$, how does that change once I parameterize it?

$$\int \int \int (x^2+y^2)dxdydz$$ where $$ \\~\\y^2+z^2 \leq x, \\~\\ 0 \leq x \leq h$$

EDIT: Would the $y$ bounds go from $0$ to $r cos (\theta)$, and the $z$ bounds go from $0$ to $r sin (\theta)$? I am pretty sure the $x$ bounds go from $0$ to $h$. But from here, do I plug in $x=h$ into $x^2$ and $y=rcos(\theta)$ for $y^2$?

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    Have you tried cylindrical coordinates? – 2017-01-31
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    @SquirtleSquad I provided an edit to what my best guess is. – 2017-01-31
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    Letting $x=x$, $y=rcos(\theta)$, $z=r\sin(\theta)$, your new bound will be $0 \leq \theta \leq 2\pi$, $0\leq r \leq \sqrt{x}$, and $0\leq x\leq h$ – 2017-01-31
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    In other words, you want to integrate in $x, \theta, r$ not $x,y,z$. – 2017-01-31
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    the integrand function (density) is $x^2+y^2$ (constant in $z$) or $(x^2+y^2+z^2)$ ? and where is the paraboloid you are talking about? – 2017-01-31

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