Page 200 - How To Solve Word Problems In Calculus

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becomes

b

2 2
V = π y − y 1 dx
2
a
EXAMPLE 7
2
Find the volume obtained if the region bounded by y = x and
y = 2x is rotated about the x axis.

Solution

4 4
(x, y )
2
(x, y )
1
(x,y )
2

dx
(x,y )
1
2 2

First we must determine the points of intersection of the two
curves.

2
x = 2x
2
x − 2x = 0
x(x − 2) = 0
x = 0 x = 2

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