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Find the volume generated by revolving the regions bounded by the given curves about the $x$ -axis. Use the indicated method in each case.$$y=x^{2}+1, x=0, x=3, y=0 \quad \text { (disks) }$$

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 3

Volumes by Integration

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All right. So this probably have X squared plus one. Why it was X squared plus one. And they give you the bounds from Mexico, zero two, x equals three. Uh And they also give you Y equals zero. Which is kind of important because that's telling you to take this region to revolve around the X axis. Um and if you didn't know is the disk method, they go ahead and tell you because you have these perfect discs that go across. So the formula for that is pi times the function square in terms of X. Um our bounds are zero and three like they told us and it's X squared plus one. So what I would do is foil that out. So we're looking at X to the fourth plus two, X squared plus one dx. So when you evaluate this integral, you just have to add one to the exponent and then divide by your new export. So this becomes 2/3 x cubed Less x going from 0 to 3. So at this point I'd probably use a calculator. Um Just to plug in 3 to the 5th power. It's 243/5. Uh now this next one, the one of the three's cancel with this three. So just three squared is nine times two is 18. But you can double check that arithmetic and then if you plug in zero a bunch of times, just get a bunch of zeros. So as you type this in 2043 50 plus 21 change it to a fraction. I got an answer of 348 tests and then just make sure you multiply by pi Okay.

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