Question

What is the volume obtained by rotating the region enclosed by `y=11-x`, `y=3x+7`, and `x=0` about the y-axis?

Answer 1

`V= V_1-V_2=11,525pi/27`

Explanation:

Given: `y=11-x`, `y=3x+7`, and `x=0`
Required: The volume obtained by rotating about the y-axis
Solution strategy: looking at the figure we see that

`V= 2pi [int_(1)^11x(11-x)dx- int_(-2 1/3)^1x(3x+7)dx]`

`V_1 = 2pi [(11/2x^2-x^3/3)_1^11]`
`V_2 = 2pi [(x^3+7x^2/2)_(-2 1/3)^1]`
`V= V_1-V_2=11,525pi/27`