1. ## Volume

Volume between these 2 curves

y = cos(x) and y = 1/2

a) revolve around the line x= -1
b) revolve around the line y = 2
from 0 to pi/6

I dont know how to set it up.

2. Volume between these 2 curves

y = cos(x) and y = 1/2

a) revolve around the line x= -1
b) revolve around the line y = 2
from 0 to pi/6

I dont know how to set it up.
a)

Using volume by shells you have:

π = pi
V = ⌠ 2πx(f(x)-g(x))dx, where I = [a,b]

Visually, you can see f(x) is cos(x). f(x) and g(x) are the upper and lower boundaries of x, respectively. For each cross section, x represents the radius of the shell that's created by it's revolution about some axis. Generally, that line is the y-axis (x = 0), but it's x = -1, so x becomes (x+1).

V = 2π⌠(x+1)(cos(x)-(1/2))dx, where I = [0, π/6]

b)

Apply the same principles here.

3. for b) is it the washer method?
Originally Posted by blackcompe
a)

Using volume by shells you have:

π = pi
V = ⌠ 2πx(f(x)-g(x))dx, where I = [a,b]

Visually, you can see f(x) is cos(x). f(x) and g(x) are the upper and lower boundaries of x, respectively. For each cross section, x represents the radius of the shell that's created by it's revolution about some axis. Generally, that line is the y-axis (x = 0), but it's x = -1, so x becomes (x+1).

V = 2π⌠(x+1)(cos(x)-(1/2))dx, where I = [0, π/6]

b)

Apply the same principles here.