ozgunozgur
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 Joined
 Apr 1, 2020
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 23
Hello there, can you help me to solve this problem? Thanks.
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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.
Sorry but I didn't understand which boundaries I need to take. Could you solve all?You found the antidefivative of the integrand, but you need to evaluate a definite integral.
Thank you so much, sir. At the other part(yaxis), 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:
\(\displaystyle x^2+4=4x\)
\(\displaystyle x^24x+4=0\)
\(\displaystyle (x2)^2=0\implies x=2\)
Hence:
\(\displaystyle V=\pi\int_0^2x^48x^2+16\,dx=\frac{256}{15}\pi\)
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?
Please Google those terms:I found 8 pi. Is this correct? What is the difference between washer and shell method?
Let me check:I found 8 pi. Is this correct? What is the difference between washer and shell method?