Page 135 - Calculus Demystified

The Integral
CHAPTER 4
122
7. For each function in Exercise 6, calculate the positive area between the
graph of the given function and the x-axis over the indicated interval.
8. In each part of Exercise 6, calculate the signed area between the graph of
the given function and the x-axis over the indicated interval.
9. Calculate the area between the two given curves over the indicated interval.
2
2
(a) f(x) = 2x − 4, g(x) =−3x + 10 −1 ≤ x ≤ 1
2
(b) f(x) = x , g(x) = x 3 0 ≤ x ≤ 1
2
(c) f(x) = 2x, g(x) =−x + 3 −3 ≤ x ≤ 1
(d) f(x) = ln x, g(x) = x 1 ≤ x ≤ e
(e) f(x) = sin x, g(x) = x 0 ≤ x ≤ π/4
x
(f) f(x) = e , g(x) = x 0 ≤ x ≤ 3
10. Calculate the area enclosed by the two given curves.
(a) f(x) = x, g(x) = x 2
√
(b) f(x) = x, g(x) = x 2
4
(c) f(x) = x , g(x) = 3x 2
2
4
(d) f(x) = x , g(x) =−2x + 3
4
4
(e) f(x) = x − 2, g(x) =−x + 2
2
(f) f(x) = 2x, g(x) =−x + 3