They Put An Innocent Looking Integral On AP CALC BC FRQ 2019
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- Опубликовано: 25 авг 2024
- AP Calculus BC official released FRQ 2019, secure-media.c...
Solutions to other problems by Oon Han: • AP Calculus BC Exam: FRQ
Guess when did I take my AP CALC test?
Part a) slope of the tangent line, 1:05
Part b) integral by partial fractions, 3:55
Part c) type two improper integral, 7:41
another video similar to part c: • Innocent looking, but ...
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blackpenredpen
100/(1-x)
Amazing!!!
Thanks!!!
Oon Han how are you this early
@@iiiiii4064 ikr
@骑士黑暗 Sounds like a racist with no brain :/
We leave the roots at the denominator because we are adults, I love you man
lol, i dont think most people who write ap exam are adults
@@Richard-yw9ew he said that in the video
@@VincentKun oh, my bad
骑士黑暗 tf?
@骑士黑暗 That's just not funny, I don't know how you find that remotely amusing.
I said it diverged on the test and a bunch of my friends were saying they had -8 or something like that so I was very nervous. Good thing I trusted the calculus!
On that question I said screw it because I didn't know what to do
Anytime I see a something that can have a V.A. i always find them then check the bounds for the integral. Funny thing, the graph was above the x-axis for 0 to 1 so it couldn't have been negative. Great job
If you're integrating something that's *squared* and you get a negative answer, you've definitely screwed up somewhere.
@@MisterSarcastic ^^^yeah basically lmao the graph is easy to visualize in your head, since it is squared it definite ly cannot be below the x axis
@@user-zc1ic5wf1s yeah i wanna know that too
You did your AP Calc BC Exam in 1942
Yea
blackpenredpen 2003 :)
@@blackpenredpen can you do the frq on the bc late exam?
1989?
Obviously not. If he took the test in 1942 he wouldn’t be alive now because the Japanese were bombed in 1945
I was on so much adrenaline I somehow solved this entire question. I look back at it now and somehow do not remember how to solve
Jordan Lin I cheated I used a scientific calculator on this test :P (it can do derivatives and integrals it just can’t graph but the upside is I’m 5x faster with it) my Ab teacher didn’t mind but my bc teacher would get mad and embarrass me in front of my class every single test.
h_ What calculator were you using?
- ThiccTiddiesInc - ti-36x pro
Math can get pretty intense
How did he just make math enjoyable and charming?
This calc bc test tomorrow has got me worrrieeddd
How did it go?
"We can leave the square root in the denominator on the AP test *because we're all adults now*" Tell my alma mater that.
: )
Granted it was calc AB so
The_Iscariot so my geometry lied when I had to rationalize the denominator
Just saying, when I was in AP Calc, sometimes we'd get assigned old FRQ's as homework. If you just worked out the FRQ's for each AP test (AB and BC) when they are released, you could have a really popular playlist.
12:41 "Here we have positive" - pointing at "-1" ;)
Swear I read this comment right as he said it in the video
Very clear! I think you took AP exam just feeeeeeeeeww years ago, still young man 😂
Mak Vinci lol thanks!!
I honestly have no Idea if I got this right, as after leaving the testing room I immediately blocked everything in there out of my mind...
except for that damn polar question.
That polar question was sick. I got it right cause of 3blue1brown.
A master who can make your concepts crystal clear.
Wait... How did I actually get this question right?
Probably from watching bprp 😎
: )))))
How old are Americans when they take this?
@@theomc1488 16, or 17. Only small fraction of people take it though
@@karolakkolo123 ooo. In the uk 17 to 18 year olds take a test called Further maths. Does Ap calculus just do calculus or does it do other parts off maths?
@@theomc1488 It only does single-variable calculus, basic infinite series concepts and convergence tests, and then some calculus with parametric equations and polar coordinates. But that's it
Who’s here on Christmas Day?
No one?
Katie S Idk how I got here but I’m here as well lol
yep
im here somehow
Convenient
Missed this by 1 day
I remember doing this question on the actual test and making a silly mistake on part C, was a fun question.
This video is what wil make you famous amongst students studying for Olympiads (other than the #100 series)!
C. D. Chester haha thanks!!
part (b) is also -arccoth(3)/3 (= -(ln 2)/6) by completing the square.
I feel bad, i completely overlooked the vertical asymptote on part c. That is one of three points i missed on the free response.
Why the hell does that matter? Isn't your wife a doctor?
Ben Shapiro Math doesn't care about your feelings ben shapiro
MANYMANYMANYMANYMANY years ago
*many intensifies*
Just take the limit as MANY approaches infinity XD
For part (c) the function is symmetric about x=1 So both parts of the integral are equal.
Both parts also diverge to positive infinity
question b
x^2-2x-8 = x^2-2x+1 - 9
= (x-1)^2 - (3)^2
then use the inv tanh formula
-1/3 tanh^-1((x-1)/3), evaluate from 0 to 1
answer -1/3 tanh^-1(-1/3)
Wow. I’m surprised how quickly I recognized that thumbnail, instantly remembering that exact question. Although it looks like I at least got part of it right, so I guess I did good.
I'm in my 4th year of university in France and I love your videos, very clear and helpful, thanks :)
I'm 2nd year pre university and these questions are cakewalk
I would like to thank you and your channel for helping me study for Calc BC.
Dude I’m in eighth grade and I gotta take this class because I took calc ab in seventh grade
Reminds me of my calc 2 class, pretty simple stuff, but always amazing to think of what we can do with this calculus
I do the first question with the definition of the derivitif
XaXuser lol nice. I should do that too
Now that would be cool
I did it using the definition of the derivative and the formal definition of a limit.
For part (b), I forgot to add the absolute value signs in the natural log. But I used the properties of logarithms to combine the natural logs together and get the positive number inside the natural log sign, eventually got the same answer. Will AP get me credit for solving it in this way? At least partial credit?
I have reviewed a lot of past graded FRQs, I would speculate that you lose a point for the incorrect anti derivative, but only that one point assuming all of your other steps are correct.
I forget absolute logarithms on my test, but thats because none of the questions cared about the sign.
Ahh yes. When I was doing it, I quickly realized that it's divergent.
Hello blackpenredpen :), Im a student of mathematics at the University of Comahue Argentina, and also im a suscriber of your channel (love your videos).
For a Calculus I test they took the following integrals exercise that I could not solve:
Find (f ^ -1) '(0) (the derivative of the inverse evaluated at zero) where f (x) is the integral from 1 to x of sin (sin (t)) dt.
I would really appreciate if you could make a video solving it. Regards from Argentina, and continue like this, you are the best Math youtuber !!
I’m taking calculus in the fall, my mind can’t even fathom what’s happening in front of me lol
Same lol
I'd love to see what you are like during your regular lectures
2006? since you said many 13 times
Exactly my thoughts, with the difference that you actually counted "many"s ;)
Depends on what unit of measure "many" is because "many" does not equate to 1 year.
By this point of the exam my brain was already toasted to realize I had to use limits
ahh this was enjoying to watch. I miss my 2018 ap cal bc class lol. i achieved a score of 5 on the ap exam for both the ap & bc parts! i was really happy
Had to help a student with this the other day,
I was under the impression we had to use a comparison test or 'p'-test to prove the divergence?
Now looking back that seems a bit difficult, and both sides diverge to positive inf if I remember correctly.
Thank you, Very helpful and Great video!
You have to do one of those tests to show a series is divergent. Here, we just need to show any limit anywhere in the integral does not exist to verify the integral diverges. In this case, he showed that the limit was unbounded.
This was my favorite question from the test!
Me too!
i have used integral test on it by checking it at what value it is a decreasing function i.e at (1, infinity) then taking the integral between those and value coming out to be not defined .
I do a levels in the UK London - I love watching your calc videos
I now know where my teacher gets out homework from...
"We can have the square root in the denominator because we're all adults now"
My Applied Maths Numerics professor took this personally
That microphone snatch was so satisfying!
Thank you!!!!!
I think I got this problem right, but I probably lost a point for not including directions in my limits.
my friends hadn’t even heard of splitting an integral at an asymptote and they just looked at me like i was insane until they tried evaluating it on a calculator. then they believed me
Thank you for looking at this problem!!
I took this exam and I thought the free response was going to end me because it was so much harder than previous years.
When I saw that question on the exam I panicked, and then I pulled something out of my bag of tricks to solve it... still don't know how I did
Took it this year!!!!!!
Can confirm for part b that if you remove the disconuity at x=1, the integral equates to infinity.
Welcome to the real life. LMAO
What is the method to find the partial fraction numerators he uses?
Cover-up method
The pedantic way to do it is to split the terms and put a variable in each numerator. Then recombine the terms and solve them algebraically, essentially creating a system of linear equations separated by powers of x.
IMO, he shortcut the process a bit too much, leaving the inexperienced integral solver to fend for himself. It was otherwise a well constructed solution.
I almost got it right but I assumed that the area was finite :(
Can someone explain the cover up method he used at 5:05
Nice question and well explained solution ..thank u sir
He sounded like he took the AP Calculus test in like the 1500s
I don't understand how someone so smart can't think to get a clip-on mic
if it's symmetrical with one side diverging to +infinity and one side to -infinity is it ok to say the integral is zero?
e.g. integrate 1/x from -1 to 1 = integrate from -1 to 0 1/x dx + integrate from 0 to 1 1/x dx
Does it make sense to say:
integral from -b to -a of 1/x = - integral from a to b since 1/x is odd, and so
integral from -1 to 1 of 1/x dx = integral from 0 to 1 1/x dx - integral from 0 to 1 1/x dx = 0?
Unfortunately not in standard analysis. This is because there is no notion of symmetry and rate of approach in the formal definition of a limit. Simply put, a limit converges if the answer stays arbitrarily close to a value and not that x is actually approaching anything. So when you have two infinite expressions like in the video both must be convergent and you can not leverage the symmetry unless they were one limit.
If you suspect being able to take advantage of symmetry, go ahead and break it up into 2 limit-integrals as shown in the video. Then, for one of them, perform a u-substitution and see if you can convert it into a similar form of limit-integral as the other. In this example, if you take the first and perform the u-sub: "u=2-x" I believe you can convert the form of the one containing the "a" into the form of the one containing the "b". You can then add them together to get 2x the result of a single one of the limit-integrals. Then, since it can be shown to diverge singly, the double will also diverge. The primary reason here is that the function chosen happens to be symmetric about x=1. However, if the function in question had been anti-symmetric about the value x=1, then you could show that the two limit-integrals cancel each other out and the overall integral would then be zero.
@@andywinslow6631no you can only combine and break apart limits if they both converge in standard analysis
Glad to see that I got this one right lol. My guess is that you took your AP Calc BC test in 2004
YOU GOT IT!!!!!!
so young
I took this test... and somehow I got a 5 on it. I didn’t study at all, and I completely failed the class itself (like 28%). But whatever, person with the lowest grade aces the test.
I am going to watch more black pen red pen for BC now
Don't forget your chain Loo.... Hey, I respect you but this was so funny.
Vighnesh Raut
It’s the Chen Lu
I loved this problem. Definitely got full credit
I had been trying to solve the general form on the thumbnail; now I feel stupid.
You have a distance of 20 meter to the equal parts of each section is equal to x so that the first x---->t then the second x ----->1/2t then 1 / 4t … and so on, Calculate the total distance in terms of X, and the time took?
Wtf
Many many years ago?
No way, you look so young! I thought you were about 21!
Its been 20 years for me!
It’s been 15 years for me!
Ah, one of the weirdest things in integration. At some point, it switches from inverse tangents to natural logs
You say chain rule the exact way I say it !!! Chain Lu 😀
Jeez, it's been so long I don't even remember solving this
This actually was, and is, VERY INNOCENT! :)
These questions about calculus were the only ones i was able to solve,they others go way over my head,maybe because i havent studied them yet
I haven’t taken calculus yet why am I even watching this 💀 interesting trying to understand it with knowing anything
Raul Sotelo same!!!
They got me on the improper integral
Can you do more of these problems? I just took the test and am stressed out on if I got them or not.
Can you maybe consider doing this and also being a tutor for different math level and grades on the side like a playlist? It would help alot.
I would have got this if I took BC the AB questions were ridiculous
I was doing some practice and I managed to solve the first two parts flawlessly and then I made a dumb mistake on the improper integral which cost me 2 points :P
Hey man I love your videos! can you please solve the other 2019 calc bc frqs?
The year that you took the BC test diverges
1994? random guess
I took this exam, this problem killed me while I was taking it
3B1B and this channel are all good mathmatics producer
xpllmmff thank you!!
could you use a limit comparison test for 5c? I'm not familiar with using one when one of the bounds aren't to infinity.
6:32 You could (and are encouraged to) stop working as soon as you plug in the numbers, because on the AP test your answers don't have to be simplified.
With this reasoning, you can stop working at any point you want, even at the beginning of the problem, just after having written the first line.
+MarcoMate87 No; you cannot leave any calculus work left. For example, if you setup your answer using a definite integral, you cannot stop there unless you are told not to evaluate; you must evaluate the integral. If this means finding an antiderivative and plugging in numbers, you must plug in the numbers, but once you do this, it is simply a numerical expression that can be left unsimplified. However (and I am opposed to this), all trig functions must be evaluated.
i'm in H pre calc right now. i'm not ready for this.
Ethan A lol good luck bro not as bad as it looks but it’s bad
And for a general k?
What's really sad is that I watched the old video of the innocent looking integral the day before the BC exam, thought about that video when doing the question, and then proceeded to do it the incorrect way because I like to doubt myself :)
Omg the international exam had one as well but I’m not allowed to disclose it☹️
Yay college board!!.!...!.........
Aryaman Kejriwal wow u mean a problem like part c?
blackpenredpen it was not an asymptotic thing, but rather just ‘really hard to integrate’. Nobody at my testing centre seemed to get it.
Can someone explain to me how he took the natural log of a negative number?
Great work, private. I know I wasn't there for some of your videos .where you reside
When you see denominators in definite integral, be careful.
2010?
7:40 I thought the domain of ln was always bigger than zero what happened there
What about writing part b as 1/[ (x-1)^2 -9 ] and using tanh-1?
Jake Moll It should work too.
Angel Mendez-Rivera seems quicker to me tbh, don’t need to do a substitution for it as it’s a standard sort
Jake Moll It is more algebra, so it would not be quicker. You would need to prove tanh^(-1) is the correct antiderivative as opposed to coth^(-1), since the derivative of both is 1/(x^2 - 1), and this would depend on the interval. So this would in fact be much longer and more work instead.
Angel Mendez-Rivera tanh exists (-1, 1), coth exists (-inf, -1) u (1, inf), and you can inspect the values to see that they lie within the range of tanh? I guess at this point partial fractions becomes the faster method
You probably could, but I think the majority of people taking the test don’t know what hyperbolic functions are
There's a thing called a lapel mic. Check it out!
You completed your AP Calc BC Exam circa 1492
I tried part b with what I learnt, by using trig sub and it went very complicated. (I just finished secondary school so...)
(Part c...
What I got was something like secx=1/3
Hype for a five on BC
You got a five ?! I scored a 4 on both ! 😄
I didn't fall in this trap but my friends did.
1993?
im an AB calc kid and just finished the first semester... idk why im watching this LOL but im entertained
Wheres the clock ??