Page 198 - How To Solve Word Problems In Calculus

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y = f(x)

(x, y)

y

a b
dx

EXAMPLE 6
Find the volume of the solid of revolution obtained by revolv-
2
ing the region bounded by y = x − x and the x axis about the
x axis.

Solution

0.5 1

The graph intersects the x axis when y = 0.

y = x − x 2
0 = x − x 2

0 = x(1 − x)

x = 0 x = 1

2
The volume of each “imaginary” circular disk is πy dx and the
volume of the region is obtained by integrating, with respect

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