Page 212 - How To Solve Word Problems In Calculus

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We first find the intersection points by solving each equation for x.
2
4x − y = 0 y = 2x − 4
4x = y 2 y + 4 = 2x

y 2 y + 4
x = x =
4 2
y 2 y + 4
Now we set = and solve for y.
4 2

2
2y = 4y + 16
2
2y − 4y − 16 = 0
2
y − 2y − 8 = 0
(y − 4)(y + 2) = 0
y =−2 y = 4

The best way to proceed in this problem is to use horizontal
rectangles. The length of each rectangle may be thought of as
x 2 − x 1 and the width dy

4

A = (x 2 − x 1 ) dy
−2
4 2

y + 4 y
= − dy
−2 2 4
4

1 1
= y + 2 − y 2 dy
−2 2 4
4
1 1
2
= y + 2y − y 3
4 12
−2

64 8
= 4 + 8 − − 1 − 4 +
12 12

20 7
= − −
3 3
= 9
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