009B Sample Final 3, Problem 4

Find the volume of the solid obtained by rotating about the  $x$-axis the region bounded by  $y={\sqrt {1-x^{2}}}$  and  $y=0.$

Foundations:
1. You can find the intersection points of two functions, say   $f(x),g(x),$
by setting  $f(x)=g(x)$  and solving for  $x.$
2. The volume of a solid obtained by rotating a region around the  $x$-axis using disk method is given by
$\int \pi r^{2}~dx,$  where  $r$  is the radius of the disk.

Solution:

Step 1:

Step 2:

Final Answer:

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