<p>So today I was taking the first practice test in the PR Calc book (for AB Calc) and two of the questions were specifically about topics I thought were excluded from calc AB-- the shell method and integration by parts. Are these topics actually on the test? I'm very confused because my teacher had told the class that both were not tested... so is PR incorrect/ simply being more difficult than necessary or is my teacher mistaken? Thanks in advance!</p>
<p>I would learn it just in case, integral by part isn’t really hard.</p>
<p>Integration by parts is not on the AB test.</p>
<p>Nope it is not.</p>
<p>i learned both in my AB class. you need to FOR SURE learn shell. it’s definitely the easiest of the three, and some MC questions will need to be converted to y values. if you don’t know both washer/disc and shell, there is no way you’ll be able to solve it (i think). I’d learn parts too. It’s kinda complicated and might require doubling back to substitution, but I’ve encountered some of problems where I have no idea what to do other than use parts. Hope this helped!</p>
<p>just learn it. it’s so easy, really.</p>
<p>It was my understanding that neither the shell method nor integration by parts were on the AP Calculus AB exam. To convert to y-values, you just set the equations, given in terms of y, equal to x.</p>
<p>yeah, i’m pretty sure that the shell method isn’t tested on the AB exam.</p>
<p>Shell method is not tested, but it is useful and you can substitute it for the disk-method. It is allowed, and the person received his/her full points for that on a recent FRQ.</p>
<p>Shell method is NOT tested on the AP Calculus exam. As some posters have mentioned, you MAY use the shell method on the exam if you know it. While some volumes questions cannot actually be done by discs/washers, every AP exam volume question will be able to be done using either discs or washers.</p>
<p>Integration by Parts IS on the AP Calculus BC exam, but IS NOT on the AP Calculus AB exam.</p>
<p>Both topics were on the AP Calculus AB exam prior to 1998, though, so some of the older tests may still test on these topics. Also, since many prep books focus on both AB and BC topics, that might explain the integration by parts piece.</p>
<p>The problem had to be solved by the shell method because you couldn’t find the outer and inner radii because there was no way to describe them from the limits of the shape. I solved the y formulas in terms of x, but the two graphs didn’t intersect at the two ends so I don’t know what I should have done…</p>
<p>EDIT: Here, I’m going to post the problem to see what you guys think… the part that was messing me up was that, like I said above, the graphs didn’t intersect at both points so when you try to find the outside radii using the washer method, you would have to use two graphs or something… Would I have to convert the x description of the limits to y values to do this?</p>
<p>The question is (hopefully this is legal to post this, haha):
The volume generated by revolving about the y-axis the region enclosed by the graphs y=9-x^2 and y=9-3x, for 0=<x=<2, is…</p>
<p>While it certainly would be easier to do the question you cite using shells, it wouldn’t be required. From y = 3 to y = 5, the outer radius would be 2 and the inner radius would be x = (y-9)/3, whereas from y = 5 to y = 9, the outer radius would be x = sqrt(9-y) and the inner radius would be x = (y-9)/3.</p>
<p>But they don’t ask questions anymore on the AP Exam where a disc/washer solution would be this much more difficult than a shells solution, and they haven’t in 12 years.</p>
<p>Thanks so much, MathProf! I think it would be x=(9-y)/3 but I get the gist of what you said, and I think it gives me the right answer so that’s really helpful! </p>
<p>So do you think PR was just giving an old practice test then? Because it also had integration by parts…</p>
<p>You’re right. That’s what I get for not writing my computations down. :)</p>
<p>It might be an old practice test. Not sure how old the review book is, but I know I saw some old review books in circulation that date back to 1997…</p>
<p>Soooo easy. “uv - Int(vdu)”</p>