M You X C InP X 2 Log X U Dig x eTe X Con X Stuc X P CM X C Way X Voll X & InVE X G . y = X y! . y= x VR Sol X N. SOL X + X -> C A learn.umgc.edu/content/enforced/738981-ORT_005902/Calculus%2011_Full%20e Text.pdf ContemporaryCalculus 120 / 388 100% + 406 APPLICATIONS OF DEFINITE INTEGRALS 117 5.2 Problems In Problems 1-12, find the volume of the solid gener- 32. Use calculus to determine the volume of a sphere ated when the region in the first quadrant bounded of radius r. (Revolve the region bounded by the by the given curves is rotated about the x-axis. x-axis and the top half of the circle x2 + y? = 12 about the x-axis.) 1. y = x, x =5 2. y = sin(x), x = n 33. Compute the volume swept out when the top half 3. y = cos(x), x = 4. y = 3-x of the elliptical region bounded by , + 32 = 1 118 5. y = v7-x 6. y = V9 -x is revolved around the x-axis (see figure below). 7. y =5-x2 8. x = y2 -9 9. x = 121 - y2 10. x2 + 12 = 4 11. 9x2 + 25y2 = 225 12. 3x2 + 5y2 = 15 In Problems 13-30, compute the volume of the solid formed when the region between the given curves 34. Compute the volume swept out when the top half is rotated about the specified axis. of the elliptical region bounded by 2 yz 119 13. y = x, y = x about the x-axis 5 = 1 is revolved around the x-axis. 14. y = x, y = x* about the y-axis 15. y = x, y = x* about the y-axis 35. Compute the volume of the region shown below. 16. y = x2, y = x* about the x-axis 17. y = x, y = x about the x-axis 18. y = sec(x), y = 2cos(x), x = 3 about the x-axis 19. y = sec(x), y = cos(x), x = 3 about the x-axis 20. y = x, y = x* about y = 3 21. y = x, y = x about y = -4 120 22. y = x, y = x* about x = -4