Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
y = 2x, y = 2, x = 0

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

i dont know sorry

step-by-step explanation:

sine

step-by-step explanation: