Page 190 - How To Solve Word Problems In Calculus

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Solution
1

1 2 3 4

−1

−2

−3
The x intercepts are determined by setting y = 0 and solving
for x.

2
y = 4x − x − 3
2
0 = 4x − x − 3
2
x − 4x + 3 = 0
(x − 1)(x − 3) = 0

x = 1 x = 3
The area may then be easily computed by integrating from 1
to 3.
3

A = ydx
1
3

2
= (4x − x − 3) dx
1
x 3 3
2
= 2x − − 3x
3 1
3 3 1 3
2 2
= 2(3) − − 3(3) − 2(1) − − 3(1)
3 3

4
= 0 − −
3
4
=
3
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