Question

3 week_6 week_7 week 8 project exam week_4 week_5 Question History: O logistics other Use the regions A and B sketched below in parts (a) and (b): 3 A 2- B y=2x²+1 0 e

Answer 1

(a) (i) The sketch of the solid is shown below: (i) The cross section is a washer. At distance x, from the origin, the cross section area is A(x) = r [32–(2x2 +1)] = 7 [8–4x* – 4x2] (ii Volume of solid using washer method is V = ('4(x) dx = ( [8–4x4 - 4x2]dx (iv) Cros section area of an elemental shell is A(y) = 21 xydy = 27 ya dy. 0 Sy S3 (v) Volume of solid using cylindrical shell method is 8877 V = f*4\u)dx = [22 y/oztáv = 927 [v\v=lậy = 2027 44. 15 15 y-1 (b) (i) The sketch of the solid is shown below: (ü) The cross sections perpendicular to y-axis are disks. There are two descriptions of cross section. (i) Volume of solid using disk method is (21-8). V = [xx1?cv + L+7(1-x)” dy = 1 + dy 6 (iv) Cros section area of an elemental shell is 4(x) = 27 (1-x) y = 26 (1-x)(2x +1) .05x51 (v) Volume of solid using cylindrical shell method is 7+1=1 - 121-30 V = [ A()dx= ["27(1-x)(2+2 +1}ex = 47

R 4 yこ204) で

y=22²7 B 1