Carolina C.

asked • 12/17/23

partial fractions

find the volume generated by revolving the area bounded by y = (1/x^3+7x^2+10x), x=4, x=8 and y = 0 about the y-axis.

William W.

tutor
Please clarify the function. Is it 1 divided by the entire polynomial?
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12/17/23

Carolina C.

yes!
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12/17/23

Doug C.

Here is a Desmos graph that takes you through the solution. Look it over, take some notes, and reply with any questions you still have. The idea is to use the shell method, where average radius = x and height of a typical shell is f(x). To find the antiderivative, 1st write xf(x) as 1/(x^2+7x+10), then use partial fraction decomposition to rewrite as shown here: desmos.com/calculator/yqzjkju3ra
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12/17/23

1 Expert Answer

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Doug C. answered • 12/17/23

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