Answer:
V = 8π/3
Step-by-step explanation:
Haven't done calc in years so I might be wrong.
Graph out all the lines needed so you can have a better look at it.
I set y=2x = y=2 to find where the intersect each others so I can have my boundaries for integration.
You goal is to find the area so you can integrate around that area. We're revolving around the x-axis so the area will be a circle.
V = ∫A(x)dx = ∫(πr²)dr
Since we have two different radius, we subtract them from each others.
∫(πr₂² - πr₁²)dr
∫(π(2)² - π(2x)²)dr
∫(4π - 4πx²)dr
4π∫(1 - x²)dr
integrate from 0 to 1 since that's where our boundary is.
V = 4π∫(1 - x²)dr = 8π/3
