Applications of Integrals Review (All of AP Calculus Unit 8)

In this video we review all of Unit 8 of AP Calculus AB and BC. This includes: average value of a function; connections to position, velocity, and acceleration; accumulation functions and definite integrals in applications; area between curves; volumes with cross sections (squares, rectangles, triangles, semicircles); volumes of revolution (disks and washers); arc length (BC Calc only!)
Time Stamps:
00:00:27 (8.1) Average Value of a Function
00:04:10 (8.2) Connections to position, velocity, and acceleration
00:09:00 (8.3) Accumulation function and definite integral applications
00:14:11 (8.4, 8.5) Area between curves
00:24:39 (8.6) Area between curves that intersect more than once
00:29:14 (8.7, 8.8) Volumes with cross sections (square, rectangle, triangle, semicircle)
00:43:03 (8.9, 8.11) Volumes of revolution around x and y axis (disks/washers)
00:49:34 (8.10, 8.12) Volumes of revolution around other axes
01:00:59 (8.13, BC Only) Arc length of a function
You'll run into all of these ideas as you go through Calculus 1 and Calculus 2 in typical college courses as well. Everything in here could show up on the multiple choice or Free Response section of the AP Calculus exam.
#apcalculus #review

[@lucasawad6602]

Back again, thank you for making calculus doable to revise! My friends and I really appreciate you!

[@turksvids]

Nice! I can tell your working hard. I hope it's paying off!

[@danial1113]

Stuff I don’t fully understand in weeks at school makes so much sense when you explain!

[@turksvids]

Happy to help!

[@lilac-8442]

absolute banger vid thanks so much for this

[@turksvids]

thanks! please share with anyone you think it might help!

[@prosaicGodowsky]

Thank you so much your videos explain this unit so well!

[@gabeb6889]

You are a goat and a scholar. Thank you.

[@SaltJackalope]

Very helpful

[@nathanxabrera6169]

great vid helps alot :)

[@lucasawad6602]

Man you are such a life saver

[@cardude1414]

facts

[@arkap8596]

Test tomorrow after being sick for a week and a half, my friend sent me this to try and help, thank you and I hope I don’t bomb this thing

[@turksvids]

hope you feel better and ace your test! good luck!

[@zainanwar6827]

Thanks Beast.

[@mely1056]

thank you! would love to see a review vid for unit 9 & 10 :D

[@brxyann]

underrated

[@dreamsbyiris]

thank you!! great review for my unit 8 test tmrw🙏

[@turksvids]

hope the test went well! good luck studying for the exam!

[@hellohi-mj8ho]

Your videos are very human thank you

[@turksvids]

Thank you! Good luck with your studies!

[@ashvinjaishankar3813]

Regarding the arc length example you did with a left Riemann sum: if you were told that f’(x) is strictly increasing (or decreasing), could you be asked if the approximation of the arc length of f is an overestimate or underestimate? Or is that based on the concavity of the function?

[@turksvids]

(I confess to not actually looking at the problem, but I'm assuming f is the function we're finding the arc length of...) this is a good question. I'm sort of thinking it through as I type. Once we write the integrand we have a new function that we're approximating.so if that function is increasing/deceasing we'll know what kind of error we get. Is knowing f' is increasing/decreasing enough to tell us that? I seems like it, f' increasing tells us f'' is positive (let's say), so if the integrand is g = sqrt(1+(f')^2) then g' = f''/sqrt(1+(f')^2). the denominator is always positive, so the whole sign of this is determined by the sign of f'', which we know. So I think it's enough info! What do you think?

[@ashvinjaishankar3813]

@@turksvids that was my thought as well, except I think the numerator of g'(x) would be f''(x) * f'(x) by the Chain Rule

[@turksvids]

Of course! Forgot the chain rule…that’s embarrassing. Good thing it was only on the internet!

[@Ak-bl3tq]

fire video im passing calc

[@sparks4384]

damn calculus is hard

[@asiananduuu3166]

turksvids is my goat

[@turksvids]

happy to help!

[@danhimelstein1439]

29:15 Volume with Cross Sections

[@turksvids]

In case you need/want them:
00:00:27 (8.1) Average Value of a Function
00:04:10 (8.2) Connections to position, velocity, and acceleration
00:09:00 (8.3) Accumulation function and definite integral applications
00:14:11 (8.4, 8.5) Area between curves
00:24:39 (8.6) Area between curves that intersect more than once
00:29:14 (8.7, 8.8) Volumes with cross sections (square, rectangle, triangle, semicircle)
00:43:03 (8.9, 8.11) Volumes of revolution around x and y axis (disks/washers)
00:49:34 (8.10, 8.12) Volumes of revolution around other axes
01:00:59 (8.13, BC Only) Arc length of a function

[@kelvisaisawesome]

6:44 what…? ☹️

[@turksvids]

it's a thing!

[@kelvisaisawesome]

@@turksvids “gretchen, stop trying to make “fetch” happen. It’s never going to happen!”
… but it happened…