#16 2019 MIT Integration Bee Final

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derivative y=f(logb(arc tan(px+q))

2:13

derivative y=f(logb(arc tan(px+q))

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logic: tautology (¬p→q)∧(¬p→¬q) →p

4:10

logic: tautology (¬p→q)∧(¬p→¬q) →p

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

1:49

1st way: exp ∫(e^x)/x (1+x log(x)) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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Swinburne U 2nd way: e^(-e^x) e^x dx

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Swinburne U 2nd way: e^(-e^x) e^x dx

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Review: Linear form, Quadratic form & Bilinear form

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Review: Linear form, Quadratic form & Bilinear form

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

1:23

A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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2nd way: integral ∫ log √x(x^n) dx

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2nd way: integral ∫ log √x(x^n) dx

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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If sec(x+y)=xy then find dy/dx

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If sec(x+y)=xy then find dy/dx

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2nd way: log sqr integral ∫ln(x)/x dx

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2nd way: log sqr integral ∫ln(x)/x dx

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Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction

3:27

Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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2nd video: 🇪🇹Yemariam🇪🇹 [Draw a person with top hat with digits ...]

1:43

2nd video: 🇪🇹Yemariam🇪🇹 [Draw a person with top hat with digits ...]

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Lamar U 2nd way: evaluate trig integral ∫x sin(x^2) [cos^4(x^2) + 8 cos^2(x^2)-10] dx

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Lamar U 2nd way: evaluate trig integral ∫x sin(x^2) [cos^4(x^2) + 8 cos^2(x^2)-10] dx

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2nd way: integral ∫(6+4x--2x^2) dx via 1) complete sq 2) then trig. sub

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2nd way: integral ∫(6+4x--2x^2) dx via 1) complete sq 2) then trig. sub

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2 ways: derivative (ax+b)^n

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2 ways: derivative (ax+b)^n

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1st/2 ways: integral ∫1/(x(x^n -1)) dx

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1st/2 ways: integral ∫1/(x(x^n -1)) dx

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AP Calculus: log ∫√x(√√x) da

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AP Calculus: log ∫√x(√√x) da

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2nd way: sqrt trig integral ∫1/(√x cos^2(√x)) dx

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2nd way: sqrt trig integral ∫1/(√x cos^2(√x)) dx

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