2024 MIT Integration Bee Final

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Screen Recording 2024-05-13 at 9.18.43 PM

1:10

Screen Recording 2024-05-13 at 9.18.43 PM

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

2:30

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

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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

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

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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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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(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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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(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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integral ∫ x dx withOUT using Power rule.

1:32

integral ∫ x dx withOUT using Power rule.

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Variability or spread of a distribution. Whey we need it!

3:58

Variability or spread of a distribution. Whey we need it!

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prob stat The events A & B are s.t P(A)=5/12, P(B)=2/3 & P(A' n B')=1/12.

4:48

prob stat The events A & B are s.t P(A)=5/12, P(B)=2/3 & P(A' n B')=1/12.

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UC Davis #1: 2 ways Find the length of the graph for y=3x+2 on the closed interval ...

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UC Davis #1: 2 ways Find the length of the graph for y=3x+2 on the closed interval ...

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2 ways: integral ∫ 1/(x^2 √(1+x^2)) dx

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2 ways: integral ∫ 1/(x^2 √(1+x^2)) dx

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2 ways: exp derivative a^(logb(cos(px+q))

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2 ways: exp derivative a^(logb(cos(px+q))

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prob stat: Consider the experiment of tossing a fair coin twice & reading the up face on each toss.

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prob stat: Consider the experiment of tossing a fair coin twice & reading the up face on each toss.

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Screen Recording 2024-05-11 at 8.48.24 PM

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Screen Recording 2024-05-11 at 8.48.24 PM

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Median [special weighted mean]

4:35

Median [special weighted mean]

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1st/2ways: Taylor series of sin(x)

6:50

1st/2ways: Taylor series of sin(x)

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