Volume of intersection of cylinders using polar coordinates

Asked May 18 '15 at 15:58

Active Jan 22 '19 at 11:01

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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?

edited Jan 22 '19 at 11:01

asked May 18 '15 at 15:58

Ting Kian Rong

1

you don't need calculus to solve this problem, see this answer for a related question. – achille hui May 18 '15 at 16:12
if i want to use the integral way to solve it, can you give me some hint ? – Ting Kian Rong May 19 '15 at 13:58
You can translate above answer to a triple integral and then integrate over $y$ and $z$ first... i.e. $$\int_{-2}^2 \left[
\int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} dy dz \right] dx$$ – achille hui May 19 '15 at 14:07
can i use polar coordinates to do it ? will it be easier to solve right? – Ting Kian Rong May 19 '15 at 15:21
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. – achille hui May 19 '15 at 19:51
can u show me your working ? – Ting Kian Rong May 20 '15 at 13:12
Aside from the existing links, this comment is to link this post as one of the (abstract) duplicates to the current choice of mother/target post. – Lee David Chung Lin Jan 22 '19 at 10:59

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