Should I rotate it separately for three of them?You need to submit an attempt at solving the problem, and we can help you where you are stuck. In the mean time, I can get you started.
In both parts, start by making a graph of the 3 equations and shade the region that is bounded by them.
Then both questions can be solved using the disk method for volume.
Thank you so much, sir. At the other part(y-axis), will the boundaries need again 0 and 2, and x will be equal to 2?No, the strips run from \(x=0\) to \(x=2\). We are given the lower bound, since the vertical line \(x=0\) is one of the boundaries of the shaded region. The upper limit fomrs from there the quadratic and linear functions intersect:
\(\displaystyle (x-2)^2=0\implies x=2\)
I found 8 pi. Is this correct? What is the difference between washer and shell method?When revolving about the \(y\)-axis, I would use the shell method, where:
\(\displaystyle dV=2\pi x((x^2+4)-4x)\,dx\)
Do you see that the radius of an arbitrary shell is \(x\) and the height is the difference between the quadratic and the line?
Let me check:I found 8 pi. Is this correct? What is the difference between washer and shell method?