Use a double integral to find the volume of the solid bounded by two surfaces $$x^2+y^2=4,$$ and $$x^2+z^2=4.$$

is it using one way to integrate or there is using separation way?

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    $\begingroup$ you don't need calculus to solve this problem, see this answer for a related question. $\endgroup$ – achille hui May 18 '15 at 16:12
  • $\begingroup$ if i want to use the integral way to solve it, can you give me some hint ? $\endgroup$ – Ting Kian Rong May 19 '15 at 13:58
  • $\begingroup$ You can translate above answer to a triple integral and then integrate over $y$ and $z$ first... i.e. $$\int_{-2}^2 \left[ \ \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} dy dz \right] dx$$ $\endgroup$ – achille hui May 19 '15 at 14:07
  • $\begingroup$ can i use polar coordinates to do it ? will it be easier to solve right? $\endgroup$ – Ting Kian Rong May 19 '15 at 15:21
  • $\begingroup$ You can use polar coordinates but it will be a bad choice for this particular problem. The integral over $y$ and $z$ above give you 4(4-x^2), integrating a polynomial is much simpler than integrating any trigonometric function. $\endgroup$ – achille hui May 19 '15 at 19:51

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