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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

y=5+1/(x^2), y=5, x=3, x=6; about the x-axis.

I'm not sure how to solve this because there are four curves that we're dealing with in the question.

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HINT

Make a sketch and note that

  • for $x=3 \implies y=1+\frac1{x^2}=\frac{10}9$
  • for $x=6 \implies y=1+\frac1{x^2}=\frac{37}{36}$

therefore the set up is

$$V=\int_a^b \pi \left(y_{max}(x)-y_{min}(x)\right)^2 dx$$

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