Question

2. Set up an integral to find the volume of the solid generated when the region bounded by y = 2x² and y = x³ is

(a) Rotated about the x-axis using shells

(b) Rotated about the x-axis using washers

(c) Rotated about the y-axis using shells

(d) Rotated about the y-axis using washers

(e) Rotated about the line x = −3

(f) Rotated about the line y = −2

(g) Rotated about the line y = 11

(h) Rotated about the line x = 7

Answer 1

Set X3 2x 'c2,) 2 sing Sholls For thisArsa wi funtion f y (a) Retated about x-akis (2,8) g's Ay= 2y) (2.-2n (2-yb) 2 3/2 (Rtatd aboutakis usirg shally Por this Areu i ntion

(x3-2x) AC 2T X Ad V= 2x3) d 2 rt uirng uasher bRotated about -xs ) AC) 7t 4)dx V cd Rtated aboct y-anis using washurs Ag)E7 Ceys 2 2 V

Rated abprtneime geit2 (Retatd about the line y -2 utey adius- -2-2x 9 1adios = -2-x3 M2x A) 2-)-2-22 8 -2K3 C9 Rotated about the ling ej= l Outen Radius I1-22 Inney sadiug AC) -2-}Jdx

Rotatedabot ne 2x2 g's +3 Inner ndius 33 ,(28) 3 3+3, 2 Vs h) Rotated about line 7 Outer 91adius Mner sadiuss7 (2,9 VE 7