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#10 2024 MIT Integration Bee Qualifying Exam

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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n
5:12

UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n

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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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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(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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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
0:53

MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...
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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...

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review: When to use ... Sum of A.P n/2(a+l) vs n/2(2a+(n-1)d)
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review: When to use ... Sum of A.P n/2(a+l) vs n/2(2a+(n-1)d)

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UC Davis: differentiate y=2^cot(x)
1:02

UC Davis: differentiate y=2^cot(x)

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#9 2023 MIT Integration Bee Qualifying Exam
2:05

#9 2023 MIT Integration Bee Qualifying Exam

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#2 2023 MIT Integration Bee Qualifying Exam
1:13

#2 2023 MIT Integration Bee Qualifying Exam

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UC Davis: 2nd way differentiate y=x^(e^x)
1:29

UC Davis: 2nd way differentiate y=x^(e^x)

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alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"
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alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"

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#3 2017 MIT Integration Bee Qualifying Exam
0:55

#3 2017 MIT Integration Bee Qualifying Exam

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Growing patterns #3
4:55

Growing patterns #3

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prob stat: The prob. that it will snow tomorrow is 0.75.
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prob stat: The prob. that it will snow tomorrow is 0.75.

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UC Davis #12: exp integrate ∫(27e^(9x) + e^(12x))^(1/3) dx
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UC Davis #12: exp integrate ∫(27e^(9x) + e^(12x))^(1/3) dx

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2
3:16

Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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Digital Dance
1:43

Digital Dance

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2 ways: log exp derivative ln(x) e^(2ln(x))
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2 ways: log exp derivative ln(x) e^(2ln(x))

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RPET-91 2nd way trig integral ∫(cos(x)-cos^3(x)) dx
1:13

RPET-91 2nd way trig integral ∫(cos(x)-cos^3(x)) dx

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