math

Math 005A Homework #7

Let f(x) = (x – 2)2 and g(x) = 4 – x2. A) Find the points of intersection.

B) Find the area bounded by the curves.

C) Find the volume of the right cylinder with base bounded by f(x) and g(x) and height 6.

D) Set up an integral for the volume of the solid formed when the region is rotated about the y- axis. E) Set up an integral for the volume of the solid formed when the region is rotated about the line x = 4

F) Set up an integral for the volume of the solid formed when the region is rotated about the line y = 3

f) ⼆ 㸪 2㐺2)= 0

i. 4-炸⽕⽔ 中啙 = 0ix-omdzarebothtuahesteli-4xtuifx-z.ioMakezxlxzkoestablisn

2⽔-4X = 0 X =2

1⽐) = 9⼼ 仁 2 㤡必 我 4⾮奸 4x - 4⽐

x = 0 . 2 9 12) = 4- 12) 2

=zfxhxtxdxx-y.gsyzo 利 = 4- 1012 i. 1 0 . 4) adlz.co)

= -2 泓吼什么动州 924 Aru-f4-idx.fix_x = z的:)+4问: )

= 1: 4-州州⼭ ⼆ 鸡洲州站) =鹗 412卦⼀鎸 了-8

Vohume-AuuofB.ee xhgh - 6 2 = 16mi

性必 纠 ⼼

炸4 - 4 圻 = x -2

X -Fy X = 2 可

柳⼆厕 徘2可

G) Set up an integral for the volume of the solid with base on the xy plane, bounded by f(x) and g(x), and cross-sections perpendicular to the x-axis isosceles right triangles, with hypotenuse on the xy plane.

H) Set up an integral for the volume of the solid with base on the xy plane, bounded by f(x) and g(x) with cross-sections perpendicular to the Y axis semicircles. You must set this up as a y- integration.