2019 AP Calculus AB Exam FRQ #5
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- Опубликовано: 11 сен 2024
- 2019 AP Calculus AB Exam Free Response Question #5
Area of a region; integral by hand; Fundamental Theorem, FTC; volume with known cross sections; volume given area of cross section; volume of revolution about a horizontal axis.
this is depressing
Found this extremely helpful (particularly part C). Studying for the exam in 2020!
online exam in 2020, wow！
We don’t have this unit tho
@@rithvikyagnamurthy6560 yeah, but a month ago we didn't know that! 2020 doesn't need this for Calc AB, does need it for Calc BC.
@@turksvids ah, I also guess that learning this topic for AB doesn't hurt cuz it is technically part of the AB portion even tho we aren't getting tested on it
This is really helpful. Thank you so much for doing the problem out! 🙏
for b, why do u have to integrate to find the volume
quick question, isn't 2:15 essentially u-substitution? if so, why are the bounds not changed?
Good question! So there are two ways to deal with definite integrals that _might_ require u-substitution. What I did was actually just find the antiderivative without doing a substitution. Since the original integral is in terms of x and my antiderivative is in terms of x, I can use the original x-bounds that we were given. (I do that more often than not if possible...but I've done a LOT of antiderivatives over the years). If you do a u-substitution and find an antiderivative in terms of u, then the bounds should be u-values. That's where you'd want to change the bounds. A third option is to just do an indefinite integral on the side, using u-substitution but then going back to x, and then use the original x-bounds because the antiderivative is in terms of x. A good last second check before finishing FTC is to ask: is the antiderivative a function of x or a function of u because the bounds should be the same as the variable. Hope this helps! Good luck on the exam!
@@turksvids wow, thank you for your reply! this helps a lot!
I literally knew my stuff but made the dumbest mistakes, let's goooo
in part c, would it be the same if i wrote the radius of each function as (g(x)-6) instead of (6-g(x)) since the difference will be squared anyways or would that be wrong
Since you do end up squaring it you're fine on that. I always try to pick the expression that gives a positive radius before squaring but it doesn't matter in terms of the numerical answer nor in terms of points for the set up. Good luck!
I was going to ask this too haha!
@@dolnop6824 Yeah, you're good if you do that.
for C, what happens to that leftover volume that is not part of the solid on the top right of the graph?
You can think of it as rotating g(x) gives you a large volume while rotating h(x) gives you a smaller volume and you are subtracting the two volumes. (That little part you're referring to is the part that rotating h(x) cuts out.)
where did you get this problem? have they published it yet?
Google should find them by now. They're released 48 hours after the exam.
ok so for part c i said pi* int from 0 to 2( (11)^2) - (11 - (H(x) - G(x))^2 would that be ok
I don't understand where that integral is coming from but if you grab your calculator and evaluate both integrals you will get the point/points if both integrals give the same result.
i loved this question. cheese
Thank.
for part a do you have to simply to get area of R because my teacher said you can just do the line thing from 2 to 0.also could you list the place where you dont have to simply is that when you do 2-----0 or after you put in the x values
If I understand your question, then I think you have to go one step farther than what you're saying but not as far as I typically go. I think you could leave your answer as it looks at 3:13 of the video. There's no need to go father. (Although I'm never sure if you're allowed to leave things like sin(pi/6) because I don't think you should be allowed to leave those but it's possible you can.) You do not need to simplify as much as I do. If you're using the FTC on a problem keep going until you get to F(b) - F(a), but you need not go farther.
Easy Cake