I'm having more Calculus troubles here. Here's the problem:(adsbygoogle = window.adsbygoogle || []).push({});

Write the definite integral that represents the area of the surface formed by revolving the graph of [tex]f(x) = 81 - x^2[/tex] on the interval [tex][0, 9][/tex] about the y axis; evaluate the integral to determine the surface area.

By knowing that [tex]f(x) = 81 - x^2[/tex], [tex]f'(x) = -2x[/tex]. I then set up the integral for surface area, and I get this:

[tex]2\pi \int_{0}^{9} (81 - x^2)\sqrt{1 + (-2x)^2} dx[/tex]

Assuming I did that correctly, I can't figure out for the life of me how to evaluate the integral. Any ideas?

Edit:I'm pretty sure I set up the integral wrong. I think it should be:

[tex]2\pi \int_{0}^{9} (x)\sqrt{1 + (-2x)^2} dx[/tex]

If so, I think I found the answer, and it comes out to be about 3068.

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# Area of a Surface of Revolution

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