Consider the following curves on the given intervals.  


b. Use a calculator or software to approximate the surface area.


y=tan x , for 0≤x≤π/4; about the x-axis 

Determine whether the following statements are true and give an explanation or counterexample. 

c. Let f(x)=12x^2. The area of the surface generated when the graph of f on [−4, 4] is revolved about the x-axis is twice the area of the surface generated when the graph of f on [0, 4] is revolved about the x-axis. 

Determine whether the following statements are true and give an explanation or counterexample. 

d. Let f(x)=12x^2.. The area of the surface generated when the graph of f on [−4, 4] is revolved about the y-axis is twice the area of the surface generated when the graph of f on [0, 4] is revolved about the y-axis.

Consider the following curves on the given intervals.  

b. Use a calculator or software to approximate the surface area.

y=cos x, for 0≤x≤π/2; about the x-axis

Consider the following curves on the given intervals.  

a. Write the integral that gives the area of the surface generated when the curve is revolved about the given axis. 

y=tan x , for 0≤x≤π/4; about the x-axis 

9–20. Arc length calculations Find the arc length of the following curves on the given interval.

x = 2y−4, for −3≤y≤4 (Use calculus, but check your work using geometry.)

9–20. Arc length calculations Find the arc length of the following curves on the given interval.

x = 2e^√2y + 1/16e^−√2y, for 0 ≤ y ≤ ln²/√2

9–20. Arc length calculations Find the arc length of the following curves on the given interval.

y = x^3/2 / 3 − x^1/2 on [4, 16]

9–20. Arc length calculations Find the arc length of the following curves on the given interval.

y = (x²+2)^3/2 / 3 on [0, 1]