Give an example of a region that cannot be expres…

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Problem 59

Recall from the Volume and Average Value section in the previous chapter that volume could be found with a single integral. In this section volume is found using a double integral. Explain when volume can be found with a single integral and when a double integral is needed.

Answer

We use integral as an important tool to find volume of a given shape or body. Two types of integral, single integral and double integral, both are used to find the volume. But we can calculate volume by single integral for only those shapes which are symmetrical and have an axis of symmetry. While double integral is needed to find volume of non-symmetric and more complicated bodies or shapes or volume under a surface, equation of which, is known.

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