Page 194 - How To Solve Word Problems In Calculus

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It is clear from a diagram that f (x) ≥ g(x) for x ε [−1, 2].

10 10
(x,y ) Only one “imaginary”
2
8 8 rectangle is shown. Imag-
ine an infinite number.
6 6
(x,y )
1
4 4

2 2

− −3 3 − 2 − −1 1 1 1 2 2 3 3
−2

We are now ready to compute the area of the region bounded
by the curves.
b

A = (y 2 − y 1 ) dx
a
2

= [ f (x) − g(x)] dx
−1
2

2
= [9 − x − (7 − x)] dx
−1
2

2
= [2 − x + x] dx
−1
x x
3 2 2

= 2x − +
3 2 −1

8 1 1
= 4 − + 2 − −2 + +
3 3 2

10 7
= − −
3 6
9
=
2
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