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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 1 , 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 Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America 2