This chapter is about using integration to find the volume of a particular kind of solid, called a solid of revolution, When you have completed it, you should
be able to find a volume of revolution about either the x or y axis.
Examples of how the graphs look like :
When the region under the graph of y = f(x) between x = a and x = b ( where x = -1 and x = 1) is rotated about the x-axis, the volume of the solid of revolution formed is
Ex .
Find the volume generated when the region under the graph of y = 1 + x^2 between x = -1 and x = 1 is rotated through four angles about the x- axis.
The phase 'four right angles' is sometimes used in place for 360º for describing a full rotation about the x -axis.
The required volume is V , where
It is usual to give the result as an exact multiple of π, unless you are asked for an answer correct to a given number of significant figures or decimal places.
Ex.
Find the volume generated when the region bounded by y = x^3 and the y-axis between y = 1 and y = 8 is rotated through 360º bout the y - axis.
More exercises will be uploaded soon!
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