- #1

BraedenP

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## Homework Statement

Find the surface area generated by rotating [itex]y=5-4x^(3/2), 0\leq x\leq 1[/itex] about x=2.

## Homework Equations

[tex]SA = 2\pi\int_{a}^{b}(r\cdot ds)dx[/tex]

## The Attempt at a Solution

I simply filled in the formula for the given question, and I'm getting stuck at integration time.

[tex]SA = 2\pi\int_{0}^{1}(2-x)\cdot \sqrt{1+\left(\frac{dy}{dx}5-4x^{3/2})\right)^2}[/tex]

Simplified, it's:

[tex]SA = 2\pi\int_{0}^{1}(2-x)\cdot \sqrt{1+36x}[/tex]

We haven't done Integration By Parts yet, so I can't "deal with" the multiplication. What I tried to do was square the (2-x) to get [itex]x^2-4x+4[/itex] and then combined the roots:

[tex]SA = 2\pi\int_{0}^{1}\sqrt{36x^3-143x^2+140x+4}[/tex]

But that still isn't a manageable integral, given that I can't use substitution or anything.

How would I go about solving this question?

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