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#5 MIT 2022 Integration Bee Qualifying Exam

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#5 MIT 2022 Integration Bee Qualifying Exam

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Penn. State U: Suppose the p.m.f of discrete random variable X is ...

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Penn. State U: Suppose the p.m.f of discrete random variable X is ...

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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.

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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.

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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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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

1:23

MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(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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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

0:57

RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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trig integral ∫1/(4-3cos^2(x)+5sin^2(x)) dx

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trig integral ∫1/(4-3cos^2(x)+5sin^2(x)) dx

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1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

4:37

1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

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UC Davis #6: ∫ (2+tan(x))^2 dx

1:42

UC Davis #6: ∫ (2+tan(x))^2 dx

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#16 MIT 2022 Integration Bee Qualifying Exam

2:03

#16 MIT 2022 Integration Bee Qualifying Exam

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exp derivative x^n w.r.t x

1:02

exp derivative x^n w.r.t x

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pascal triangle: count comb Show nCk = (n-1)Ck + (n-1)C(k-1)

2:59

pascal triangle: count comb Show nCk = (n-1)Ck + (n-1)C(k-1)

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3rd/10parts: Exclusive disjunction

4:41

3rd/10parts: Exclusive disjunction

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derivative differentiate x^x - 2^sin(x)

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derivative differentiate x^x - 2^sin(x)

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1st/2ways: logic Import-Export

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1st/2ways: logic Import-Export

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2 ways: Σ 1? where k=m to n

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2 ways: Σ 1? where k=m to n

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