Question

#35 and 43

35-38. Shell and washer methods Let R be the region bounded by the following curves. Use both the shell method and the washer method to find the volume of the solid generated when R is revolved about the indicated axis.. 35. y = x, y = x1/3, in the first quadrant; about the x-axis y = - y = 1 - about the x-axis x + 1) 37. y = (x - 2)3 – 2, x = 0, and y = 25; about the y-axis 38. y = 8, y = 2x + 2, x = 0, and x = 2; about the y-axis 39-44. Shell method about other lines Let R be the region bounded by y = x², x = 1, and y = 0. Use the shell method to find the volume of the solid generated when R is revolved about the following lines. 39. x = - 2 4 0. x=1 41. x = 2 42. y = 1 43. y = -2 44. y = 2

Answer 1

Sol. 35. using washer method, y=x and y = 's - so that x= x3 x3 = x on a(x2-1)=0 x=0,1 Because x Because x lies in el Ist quadrent - volume about a-asis = r rrrouter ) - (inner² J dx l radius) hodiny 0 => ${x?5_x2]dx : *1 [ix*-. (4-: using Shell 1 x=y so that Radius = y method, and y=xe'' x=y3 y3 = 4 4 (4²-1) [y=0, 1] aind height = y-y3 . volume = us) (height) dy : ex $919-g?) dy : 235_y" day = 251 [?- ]o - 2365 ] 47 Scanned with CamScanner IS