2024 AP Calculus BC FRQ #5

Free Response Question 5 from the 2024 AP Calculus BC Exam.
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Arc length; second fundamental theorem of calculus (2nd FTC); Euler's method; integration by parts

[@CalculusConnoisseur338]

I CAN'T BELIEVE THAT I FORGOT THE +C!!!!

[@CalculusConnoisseur338]

Realistically, how many points would one lose at maximum if one forgot +C

[@CalculusConnoisseur338]

Also, is tabulation a valid method for solving the last part?

[@yna418]

wallahi im done bro😭😭

[@Thowe]

Now u got me scared, I hope I put that +C in noooooooo

[@amistrophy]

WOE, SHAME BE UPON YE🗣🔥🔥🔥

[@sandeepsawhney1656]

For part B if we forget to say on the interval [0,pi] would we get docked?

[@turksvids]

if i had to guess i would say yes, like 1 point for the interval. i see this as a "interpret in context" kind of problem, so the bounds are important.

[@kevinguacamole5300]

yessir full score

[@Dollaboi792]

How many points would i lose if I set up the calculations for v DV and u and du correct and put down the formula for integration by parts but solved incorrectly?

[@elicoe9964]

Go look at FRQ #4 from the Calc BC 2010 exam. Most of the time, you will earn one point for setting up the integral correctly, another for antidifferentiating, and another for solving it correctly.

[@bruhcentral2655]

For part b, is it okay if we put that the integral represented the length of the curve of f(x) from x = 0 to x = pi? I dont know if we specifically had to mention arc length but I just mentioned the length of the curve

[@turksvids]

I think that is fine. (I don’t think there’s another type of length that would make that answer ambiguous.)

[@bruhcentral2655]

@@turksvidsthank you for the input! Your videos greatly helped me prepare for this exam and I appreciate that!

[@CrimsonDragon0801]

uh why is the integral of cos (t/4) -4sin(t/4)? is it not -1/4sin(t/4)?

[@turksvids]

let u = t/4 and 4du = dt so you get 4cos(u)du and integrate to get 4sin(u) which is 4sin(t/4)

[@subba5952]

What form test is this?

[@loganridley2305]

form O

[@ashvinjaishankar3813]

Part d made no sense here even though it wasn’t that hard

[@turksvids]

I feel like they are developing the exam a little differently from how they did in the past. They're hemmed into the 6 FRQs, 2 calc/4 non-calc unless they change something, but they seem to want to vary up the topics within a question more often now. In recent years, they've also kind of done that with the table problems which will have two parts referencing the table and then two parts that are basically just calculator questions sort of adjacent to the table problems.