Section 14.9 Area between Curves 8. y = 2 – x –t? 10. y = 2 – x –x', x= -3, 9. y x = 1, x = 2 (d) Your answer to part (c) can be interpreted as the area of a certain region of the plane. Sketch this region. %3D ons of y. 0 = x In Problems 31-34, use definite integration to estimate the area of the region bounded by the given curve, the x-axis, and the given lines. Round your answer to two decimal places. 11. y = e', xr = 1, E = x x= 2, 12. y = (x – 1)2' E = x 31. y= x = -2, x2 +1 13. y = *= 1, ə = x °I 32. y = x = 2, x =7 valuate limits 14. y = Vx +9, x= -9, 0 = x 15. y = x² – 4x, x= 2, x = 1, 16. y = /2x – 1, x= 1, 33. y = x- 2x - 2, x = 1, x= 3 9 34. y = 1+ 3x-x 9 = x In Problems 35-38, express the area of the shaded region in terms of an integral (or integrals). Do not evaluate your expression. 17. y =x+ 3xr?, x= -2, 7 = x r = 20. y = |x|, x= -2, x = 2 19. y = e*+1, x= 0, x = 1 35. See Figure 14.37. = + x= I x = 1, x = 2 22. y =x', x= -2, 23. y = Vx - 2, x = 2, 24. y =x + 1, x=0, x = 4 when which 30 9 = x 4, 2). y = 2x gives strip 25. Given that Xーズ= upper rtical = (x)f 16 – 2x if x > 2 4. 0. Jatermine the area of the region bounded by the graph of y = f(x), FIGURE 14.37 the x-axis, and the line x = 6 Under conditions of a continuous uniform distribution (a topic in statistics), the proportion of persons with incomes between a and t. where a 3) y = x(x-3)2 %3D 28. Suppose f(x) = (1 – x)², where 0 < x < 3. If ƒ is a density function (refer to Example 2), find each of the following. (a) P(1 < x < 2) dth the (c) P (x < 1) (d) P (x > 1) using your result from part (c) 29. Suppose f(x) = 1/x, where e < xs e?. If f is a density function (refer to Example 2), find each of the following. %3D FIGURE 14.38 37. See Figure 14.39. (b) P(x < 5) (c) P(x > 4) (@) Verify that P(e 1. Evaluate xp y = 1- x2 1our answer to part (a) can be interpreted as the area of a ertain region of the plane. Sketch this region. 3. FIGURE 14.39 c) Evaluate lim xp
Section 14.9 Area between Curves 8. y = 2 – x –t? 10. y = 2 – x –x', x= -3, 9. y x = 1, x = 2 (d) Your answer to part (c) can be interpreted as the area of a certain region of the plane. Sketch this region. %3D ons of y. 0 = x In Problems 31-34, use definite integration to estimate the area of the region bounded by the given curve, the x-axis, and the given lines. Round your answer to two decimal places. 11. y = e', xr = 1, E = x x= 2, 12. y = (x – 1)2' E = x 31. y= x = -2, x2 +1 13. y = *= 1, ə = x °I 32. y = x = 2, x =7 valuate limits 14. y = Vx +9, x= -9, 0 = x 15. y = x² – 4x, x= 2, x = 1, 16. y = /2x – 1, x= 1, 33. y = x- 2x - 2, x = 1, x= 3 9 34. y = 1+ 3x-x 9 = x In Problems 35-38, express the area of the shaded region in terms of an integral (or integrals). Do not evaluate your expression. 17. y =x+ 3xr?, x= -2, 7 = x r = 20. y = |x|, x= -2, x = 2 19. y = e*+1, x= 0, x = 1 35. See Figure 14.37. = + x= I x = 1, x = 2 22. y =x', x= -2, 23. y = Vx - 2, x = 2, 24. y =x + 1, x=0, x = 4 when which 30 9 = x 4, 2). y = 2x gives strip 25. Given that Xーズ= upper rtical = (x)f 16 – 2x if x > 2 4. 0. Jatermine the area of the region bounded by the graph of y = f(x), FIGURE 14.37 the x-axis, and the line x = 6 Under conditions of a continuous uniform distribution (a topic in statistics), the proportion of persons with incomes between a and t. where a 3) y = x(x-3)2 %3D 28. Suppose f(x) = (1 – x)², where 0 < x < 3. If ƒ is a density function (refer to Example 2), find each of the following. (a) P(1 < x < 2) dth the (c) P (x < 1) (d) P (x > 1) using your result from part (c) 29. Suppose f(x) = 1/x, where e < xs e?. If f is a density function (refer to Example 2), find each of the following. %3D FIGURE 14.38 37. See Figure 14.39. (b) P(x < 5) (c) P(x > 4) (@) Verify that P(e 1. Evaluate xp y = 1- x2 1our answer to part (a) can be interpreted as the area of a ertain region of the plane. Sketch this region. 3. FIGURE 14.39 c) Evaluate lim xp
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
14 and 22
Transcribed Image Text:Section 14.9 Area between Curves
8. y = 2 – x –t?
10. y = 2 – x –x', x= -3,
9. y
x = 1, x = 2
(d) Your answer to part (c) can be interpreted as the area of a
certain region of the plane. Sketch this region.
%3D
ons of y.
0 = x
In Problems 31-34, use definite integration to estimate the area of
the region bounded by the given curve, the x-axis, and the given
lines. Round your answer to two decimal places.
11. y = e', xr = 1,
E = x
x= 2,
12. y = (x – 1)2'
E = x
31. y=
x = -2,
x2 +1
13. y = *= 1,
ə = x °I
32. y =
x = 2, x =7
valuate
limits
14. y = Vx +9, x= -9,
0 = x
15. y = x² – 4x, x= 2,
x = 1,
16. y = /2x – 1, x= 1,
33. y = x- 2x - 2, x = 1, x= 3
9 34. y = 1+ 3x-x
9 = x
In Problems 35-38, express the area of the shaded region in terms
of an integral (or integrals). Do not evaluate your expression.
17. y =x+ 3xr?, x= -2,
7 = x r =
20. y = |x|, x= -2, x = 2
19. y = e*+1, x= 0, x = 1
35. See Figure 14.37.
= + x= I
x = 1, x = 2
22. y =x', x= -2,
23. y = Vx - 2, x = 2,
24. y =x + 1, x=0, x = 4
when
which
30
9 = x
4, 2).
y = 2x
gives
strip
25. Given that
Xーズ=
upper
rtical
= (x)f
16 – 2x
if x > 2
4.
0.
Jatermine the area of the region bounded by the graph of y = f(x),
FIGURE 14.37
the x-axis, and the line x =
6 Under conditions of a continuous uniform distribution (a topic
in statistics), the proportion of persons with incomes between a
and t. where a<i<b, is the area of the region between the curve
N=1/(b - a) and the x-axis from x = a to x = t. Sketch the
graph of the curve and determine the area of the given region.
3. Include a sketch of the region.
36. See Figure 14.38.
%3D
y = 2r
27. Suppose f(x) = x/8, where 0 <x< 4. If f is a density
function (refer to Example 2), find each of the following.
(a) P(0 < x < 1)
(b) P(2 <x < 4)
(c) P(x > 3)
y = x(x-3)2
%3D
28. Suppose f(x) = (1 – x)², where 0 < x < 3. If ƒ is a density
function (refer to Example 2), find each of the following.
(a) P(1 < x < 2)
dth
the
(c) P (x < 1)
(d) P (x > 1) using your result from part (c)
29. Suppose f(x) = 1/x, where e < xs e?. If f is a density
function (refer to Example 2), find each of the following.
%3D
FIGURE 14.38
37. See Figure 14.39.
(b) P(x < 5)
(c) P(x > 4)
(@) Verify that P(e <xse²) = 1.
ob-
y = 1
%3D
J0. (a) Let r be a real number, where r > 1. Evaluate
xp
y = 1- x2
1our answer to part (a) can be interpreted as the area of a
ertain region of the plane. Sketch this region.
3.
FIGURE 14.39
c) Evaluate lim
xp
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning