9/5/2021 Section 6.4 Areas of Surfaces of Revolution-Carrie Frizzell 4. Find the area of the surface generated by revolving x - 21/1 -y , 0sys - about the + / w (1.4) y-axis. x -2V1-y 2 Set up the integral that gives the area of the given surface. S=a. Write the integral that gives the area of the surface generated when the curve is revolved about the given axis. b. Use a calculator or software to approximate the surface area. y = tan x, for - Sxs- 8 ; about the x-axis a. Choose the correct answer below. 3x / 8 O A. 27 tan x 1 + sec 2 xdx 1 /7 3x / 8 O B. 2x x 1 1 + sec4 xdx 31 / 8 O C. 27 tan x 1 + sec 4 xdx 1/7 3nt / 8 OD. tan x 1 1+ sec 4 xdx b. The area of the surface is square units. (Do not round until the final answer. Then round to the nearest hundredth as needed.) "14. Let f(x) = /7x- x2 and let R be the region bounded by the graph of f and the x-axis on the interval [0,4]. a. Find the area of the surface generated when the graph of f on [0.4] is revolved about the x-axis. b. Find the volume of the solid generated when R is revolved about the x-axis. a. Find the area of the surface. square units. (Type an exact answer, using it as needed.) b. Find the volume of the solid. cubic units. "Type an exact answer, using it as needed.)a. Write the integral that gives the area of the surface generated when the curve is revolved about the given axis b. Use a calculator or software to approximate the surface area y = 4 sin (x), for 0sxs _ ; about the x-axis a. Choose the correct answer below. 1/3 4 sin (x)1 1+ 16 cos (x) dx #/3 O B. 2x 4 sin (x) v 1 + 16 cos (x) dx 0 1/3 O C. 2x |4 sin (x) 1 1 + 16 sin (x) dx 0 1 / 3 OD. 4 sin (x)1 1 + 16 cos (x) dx b. The surface area is approximately square units (Do not round until the final answer. Then round to the nearest hundredth as needed.)