Volume of the solid from rotating four curves

Question

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.

Answer 1

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

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