∫arccos(sin(x)) dx [0, 2π] MIT Integration Bee 2024, Qualifying Exam, Question 5 #mitintegrationbee

#mitintegrationbee #trigonometry #integrationtricks

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Questions of MIT Integration Bee
https://math.mit.edu/~yyao1/pdf/

Questions of Stanford Math Tournament
https://www.stanfordmathtournament.org/past-tests/problems

Following are some of playlist and ideos on calculus, algebra, logarithm, trigonometry and some older video on ioT/Smart Home:

MIT Integration Bee
https://www.youtube.com/playlist?list=PLTKzQhisoTW3zWbfGz1pSTKt01HW9NRrT
Area Under Curves
https://www.youtube.com/playlist?list=PLTKzQhisoTW1VbdzGbXPAn6NsV4LsQX0p
JEE-Main, India
https://www.youtube.com/playlist?list=PLTKzQhisoTW3Lebxx943NTLl6JBAlXELs
UK AQA/CIE A-Level
https://www.youtube.com/playlist?list=PLTKzQhisoTW0KzlB9XUT236qjWhZVfaDy
Stanford Math Tournament
https://www.youtube.com/playlist?list=PLTKzQhisoTW1_xC1mDA_DTXESxr5M9u1d

Calculus
[1] Solving Gaussian Integral (integration of gaussian function) by Feynman’s Method.
https://youtu.be/6hI1ij6l8e4
[2] Created another 1 minute video for Happy π day! Solve an integral and the answer is π!
https://youtu.be/0L07TwBmaeU
[3] Solving integral x^(9)*(x^(10) + 1)/(x^(20) + 1) dx. Can we solve it using substitution?
https://youtu.be/Qq1YS-X7lzQ
[4] Solving integral 1/(-sqrt(x^2 + 4*x + 3)) dx. Can it be solved by substitution?
https://youtu.be/pvD7t0BoSoY
[5] Solving sum of k=0 to ∞ for integral sin^(2k) (x) dx. Solution is much easier than expected!
https://youtu.be/3W62aJuQD70
[6] Solving area of region bounded between 2 curves, i.e., {(x,y): x^2 ≤ y ≤ x + 2} using integration.
https://youtu.be/Me7xO7-1hgw
[7] Solving integral (x^2 - 1)/(x^4 - 1) dx.
https://youtu.be/qZS2GI2b_iM
[8] Given y=kx^2, x=ky^2, k is +ve constant & area enclosed between parabola curves is 1 unit^2. Find k.
https://youtu.be/WyO7CZMBmQs
[9] Given f(x) = integral (x^5-16x)/(x^8-256) dx and f(-2) = π/32. Find f(2). Explanation in 60 seconds

https://youtu.be/Pmto_UpbDq4
Algebra
[1] Is this a quartic or quadratic problem? Can we solve it within 60 seconds and without calculator?
https://youtu.be/ePB5jHQloc8
[2] Solving (10016*104*12*8 + 256)^0.5 but without using calculator & computer. Answer is a nice number!
https://youtu.be/CJL2-I8RalU
[4] 15 seconds video on solving sqrt(10300 - 9*10*10*11) without using calculator and computer.
https://youtu.be/EjeBdp8muhw
[5] Given x^2 - x - 1 = 0, solve cos^1 ((3/2)*(7*x + 1)/(x^9 - 18*x - 13)).
https://youtu.be/1gDNnlSn3yM
[6] An infinite radical equation, i.e., sqrt(3*sqrt(7*sqrt(…))) solve by Geometric Series.
https://youtu.be/AksnWhM3h9Q
[7] If (√ 2 + √ 3)^11 = a √ 2 + b√ 3, then (a² - (3/2)*b²)^11 = ?
https://youtu.be/c5j0k6gJe0c
[8] Given (|x-3| - 4)^2 = 4. How many answers for x?
https://youtu.be/jgF-sfDacKM

Logarithm/exponential
[1] Solving a finite power equation of (ln(x))^2. The solution is surprisingly easier than expected.
https://youtu.be/HxaBJ347E2A
[2] Given that ln(3) is approximately equal to 1.099, find ln(3.1) using calculus without calculator.
https://youtu.be/5ah2UfKDOfk
[3] Solving x^(ln x) = x for real numbers. How many answers for x?
https://youtu.be/SMrlkypSOBw
[4] Solving a radical-absolute equation. Is this a quadratic equation too?
https://youtu.be/Uw34VvoSfQE
[5] Solving a logarithm-quadratic question of Stanford Math Tournament 2021. Calculator is not allowed.
https://youtu.be/FWoCkay0FhI
[6] 15 seconds video to explain the answer for ln(-1) based on principal value of trigonometry.
https://youtu.be/EFAHLvj1ngM
[7] 15 seconds video on solving x^(ln|x|) = 1/|x|. There are 4 answers for x?
https://youtu.be/GeyB3c19_KU

Trigonometry
[1] Solving a trigonometry-power equation? Solution is fairly simple and can be explained in 60 seconds.
https://youtu.be/pZOJIpHP2Ss
[2] 45 seconds video deriving cos(-θ)=cos(θ) & sin(-θ)=-sin(θ). Basic identities of trigonometry Part 5.
https://youtu.be/L-Pw6i9qPX4
[3] 15 seconds video for deriving sec^2(x) = tan^2(x) + 1. Basic identities of trigonometry Part 1.
https://youtu.be/OFFtumChJwM
[4] 15 seconds video for deriving sin^2(x) + cos^2(x) = 1. Basic identities of trigonometry Part 2.
https://youtu.be/9hIX1iWomhQ

IoT/Smart Home
[1] Smart Home: Control Autogate using Sonoff RF Bridge with eWelink App & voice command of Amazon Alexa
https://youtu.be/05x5tcF4Y8U
[2] Can We Remote Access Node-red Server from another computer? Part 1: Wireless/Wire LAN
https://youtu.be/nyqfz1EjkrY
[3] How to install Amazon Alexa App on iPhone in Malaysia or region without it in Apple Store (Feb 2021)
https://youtu.be/5ur5G90EeLE
[4] Smart Home: Security Automation Alarm System using Aqara G2H Camera Hub, Motion & Contact Sensors
https://youtu.be/DDyslVdTGfM
[5] Node-red Iot Server & Telegram bot - Part 2: Search & display photo using telegrambot (Windows 10)
https://youtu.be/tmpozByQ27c

Видео ∫arccos(sin(x)) dx [0, 2π] MIT Integration Bee 2024, Qualifying Exam, Question 5 #mitintegrationbee канала Dr. Yap Keem Siah