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#19 2019 MIT Integration Bee Final

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1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+sin^2(x)) dx
3:30

1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+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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IIT-1995 2nd way integral ∫x^5/(1+x^3) dx
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IIT-1995 2nd way integral ∫x^5/(1+x^3) dx

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prob stat a) Calculate the mean & the std deviation of 4 numbers 2,3,6,9
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prob stat a) Calculate the mean & the std deviation of 4 numbers 2,3,6,9

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Screen Recording 2024-05-12 at 8.34.35 PM
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Screen Recording 2024-05-12 at 8.34.35 PM

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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]
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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]

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U Penn: Show that the following decomposition CANNOT hold ...
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U Penn: Show that the following decomposition CANNOT hold ...

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prob stat: 2 ways The mean of five #s 2,3,5,6,8 is 4.8. Calculate the std deviation.
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prob stat: 2 ways The mean of five #s 2,3,5,6,8 is 4.8. Calculate the std deviation.

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prob stat: A candidate obtained the following results in her math examination:
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prob stat: A candidate obtained the following results in her math examination:

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prob stat: 2 ways Joe's mean mark for the physics tests for the term was 72.
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prob stat: 2 ways Joe's mean mark for the physics tests for the term was 72.

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prob stat: For events A & B it is known that P(A)=P(B), P(AnB)=0.1 & P(AuB)=0.7. Find P(A')
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prob stat: For events A & B it is known that P(A)=P(B), P(AnB)=0.1 & P(AuB)=0.7. Find P(A')

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2nd way: Evaluate ∫ 1/√(1-e^(2x)) dx
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2nd way: Evaluate ∫ 1/√(1-e^(2x)) dx

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Find the number of permutations of the letters of the word ALLAHABAD
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Find the number of permutations of the letters of the word ALLAHABAD

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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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U Penn: Evaluate trig integral ∫(sin^2(x) -cos^2(x))/(sin(x)-cos(x))^2 dx
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U Penn: Evaluate trig integral ∫(sin^2(x) -cos^2(x))/(sin(x)-cos(x))^2 dx

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prob stat It is known that P(X)=1/2 & P(Y)=1/4. Given that X & Y are mutually exclusive, find
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prob stat It is known that P(X)=1/2 & P(Y)=1/4. Given that X & Y are mutually exclusive, find

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Columbia U: 3rd way Evaluate the indefinite integral ∫1/(1+e^x) dx
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Columbia U: 3rd way Evaluate the indefinite integral ∫1/(1+e^x) dx

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Screen Recording 2024-05-11 at 8.58.53 PM
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Screen Recording 2024-05-11 at 8.58.53 PM

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prob stat: In how many ways can a hand of 4 cards be dealt from an ordinary pack of 52 playing cards
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prob stat: In how many ways can a hand of 4 cards be dealt from an ordinary pack of 52 playing cards

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Screen Recording 2024-05-05 at 11.26.15 PM
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Screen Recording 2024-05-05 at 11.26.15 PM

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