Marianne Kemp
Assignment HW11 Integrals Applications due 04/12/2012 at 11:00pm MDT
1. (1 pt) From Rogawski ET 2e section 6.1, exercise 37.
Sketch the region enclosed by the curves x−3 = 2y and x−15 =
(y − 6)2 , and compute its area.
A=
2. (1 pt) From Rogawski ET 2e section 6.1, exercise 42.
Sketch the region enclosed by the curves x = sin 3y and x = π6 y,
and compute its area as an integral.
A=
3. (1 pt) Find total area enclosed by the graphs of y =
6x2 − x3 + x and y = x2 + 7x.
9. (1 pt)
Find the average value of the function f (x) = −9/x on the
interval [1, 4].
fave =
10. (1 pt) Find the volume of the solid obtained by rotating
the region bounded by the given curves about the line x = −8
y = x 2 , x = y2
Answer:
4. (1 pt) Sketch the region enclosed by the given curves.
Decide whether to integrate with respect to x or y. Then find the
area of the region.
Answer:
11. (1 pt) Find the volume of the solid formed by rotating the
region inside the first quadrant enclosed by y = x2 and y = 3x
about the x-axis.
y = 2x, y = 3x2
Answer:
5. (1 pt) Find the area of the region enclosed between
y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.3π.
Answer:
12. (1 pt) Find the volume of the solid obtained by rotating
the region bounded by
Answer:
Hint: Notice that this region consists of two parts.
y=
6. (1 pt) Sketch the region enclosed by the curves given below. Decide whether to integrate with respect to x or y. Then
find the area of the region.
x = 144 − y2 ,
math1210spring2012-3
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, y = 0, x = 2, x = 6
x6
about the y-axis.
x = y2 − 144
Answer:
Area =
13. (1 pt) Find the volume of the solid obtained by rotating
the region bounded by
7. (1 pt) Find the average value of f (x) = cos4 x sin x on the
interval [0, 1]
y = 9x2 , x = 1, y = 0,
about the x-axis.
Answer:
8. (1 pt) In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the function
πt T (t) = 30 + 20 sin
12
Determine the temperature at 9 am.
Determine the temperature at 3 pm.
Answer:
14. (1 pt) Find the volume of the solid obtained by rotating
the region in the first quadrant bounded by
x = 0, y = 1, x = y6
about the line y = 10.
Find the average temperature during the period from 9 am to
9 pm.
Answer:
1
Referring to the figure above, find the volume generated by
rotating the region R1 about the line OA.
Volume =
15. (1 pt) Find the volume of the solid obtained by rotating
the region bounded by the given curves about the line x = 6
19. (1 pt)
x = y2 , x = 1;
Answer:
16. (1 pt) Find the volume of the √
solid obtained by rotating
the region bounded by y = x and y = x about the line x = 2.
Volume =
17. (1 pt)
Using disks or washers, find the volume of the solid obtained
by rotating the region bounded by the curves y = x2/3 , x = 1,
and y = 0 about the y-axis.
Volume =
18. (1 pt)
Referring to the figure above, find the volume generated by
rotating the region R2 about the line OC.
Volume =
20. (1 pt)
Referring to the figure above, find the volume generated by
rotating the region R3 about the line AB.
Volume =
c
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