# Volume of Solid Bounded by the cylinders $y=x^2$ and $y=z^2$ and the plane $y=1$

Find the volume of the solid bounded by the cylinders $y=x^2, y=z^2$ and the plane $y=1$

I think the integral should be: $$\int_0^1\int_{-\sqrt y}^\sqrt y\int_{-\sqrt y}^\sqrt y\ dx\,dz\,dy$$

Could someone tell me if this is correct?

• Would your integral have been any different for $y=x^4$ and $y=z^4$? – Henning Makholm Dec 16 '13 at 4:16
• @HenningMakholm I made a typo on the integral limits. Should have been $-\sqrt y \, to \sqrt y$. Is it correct now? – EggHead Dec 16 '13 at 12:46
• @user116056 Corrected my typo on the integral limits. Is it correct now? – EggHead Dec 16 '13 at 12:48
• That looks more like it -- though using a double integral to calculate the area of a square with known side length is rather overkill ... – Henning Makholm Dec 16 '13 at 12:50