<p>This was on my BC calc test:</p>
<p>Find the volume created by a sin x graph when it is rotated around the Y-AXIS</p>
<p>The y-axis part got me. Do we just use inverse sin to get the volume???</p>
<p>Shell integration by parts?</p>
<p>Yup.</p>
<p>If a function is being rotated around the y-axis, simply integrate with respect to the y-axis. If you’re using the disk/washer method, the radius would be equal to the function x with respect to y. So if y=sin(x), x=arcsin(y).</p>
<p>Whoopee! I did it right. Would the answer be around .47pi units cubed?</p>
<p>And we didn’t learn the shell method in class</p>
<p>OH MY GOD.</p>
<p>I hated this topic so much back in BC Calc 2 years ago.</p>
<p>Why did you have to bring back horrible memories?</p>
<p>Hardy-har-har. Our BC class hasn’t even reached this topic yet. Still on the beginning of Integration by Parts.</p>
<p>ughhh i love math and HATE the shell method sooooo much. The worst part is I had to do it for my math portfolio (IB Higher Level math), which my diploma is dependent on… :(</p>
<p>
Oh man, I think we did the same set of questions, were you asked a string of questions on the areal/volumetric ratios between different regions demarcated by a set of functions?
I didn’t think the volume of revolution was actually all that hard, especially since you could’ve alternated between Shell and Washer method (if you can picture it) to get the best of both worlds (so nice integrals for both sections of the last question :D)</p>
<p>
</p>
<p>It’s obviously infinite since no bounds are given.</p>
<p>= common sense</p>
<p>I was wondering about the lack of limits as well.
Edit:
Do we call them limits? I can’t remember.
Just pretend limits are the things above and below the integration sign. :)</p>
<p>The things above and below the integration sign are the limits of integration.</p>
<p>But the type of integration you want to do might depend on the bounds of the problem.</p>
<p>Thanks. I have no idea what you are talking about in your second sentence. ‘Type of integration’? Like Definite integration?</p>
<p>I mean you could use the shell method, but I would prefer to treat the rotation as a cylinder. You could probably also do a triple integral in cylindrical coordinates.</p>
<p>One thing I hated in Calculus was using the limit definition/Riemann sum of an integral.</p>
<p>Especially when I could easily integrate instead…</p>
<p>lol shell method isnt on the calc BC exam, but its taught in classes.</p>
<p>lol at riemann sums. such a pain.
i hate drawing the sigma.
and also, i call the limits of integration the interval.</p>
<p>I actually wasn’t taught the shell method in my online class, but it was in the PR book I think. I never really learned it.</p>
<p>^
I kinda like the shell method a lot more than the donut method (I think it’s called the washer method, but I think donut sounds cooler :P).</p>
<p>Now I feel weird for discussing integration techniques on the internet…yay for being a math nerd xD.</p>
<p>I always enjoyed the shell and washer methods. They’re cool.</p>
<p>It really depends on the exact problem. Some are more suited to the disc/washer method, others are more suited to the shell method or a more creative freelancing.</p>