#3 2024 MIT Integration Bee Qualifying Exam

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Show integral 1/(x(x^2+a^2)) dx = 1/(2a^2) ln(x^2/(x^2+a^2))

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Show integral 1/(x(x^2+a^2)) dx = 1/(2a^2) ln(x^2/(x^2+a^2))

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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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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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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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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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integral ∫ x dx withOUT using Power rule.

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integral ∫ x dx withOUT using Power rule.

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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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Discrete rv X has the following prob. distribution

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Discrete rv X has the following prob. distribution

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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STPM Math T Sem. 2: Ex 11.2 Given that f(x)=tan(x), show that ...

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STPM Math T Sem. 2: Ex 11.2 Given that f(x)=tan(x), show that ...

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The biker sister is so proactive! #femalebiker #BMW R1200R

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The biker sister is so proactive! #femalebiker #BMW R1200R

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Which province's residents love buying luxury cars the most?

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Which province's residents love buying luxury cars the most?

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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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Standing by and watching is also a form of violence—do you dare to look directly into the victim's e

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Standing by and watching is also a form of violence—do you dare to look directly into the victim's e

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2 ways: exp log integral ∫3^(log81(x)) dx

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2 ways: exp log integral ∫3^(log81(x)) dx

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4 ways: sum Find the sum of the values of 4+3i for i=1,2,...,100

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4 ways: sum Find the sum of the values of 4+3i for i=1,2,...,100

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2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?

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2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?

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"baby" fact: exp e^(ix)

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"baby" fact: exp e^(ix)

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"Up to this point," "has become," "art"

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"Up to this point," "has become," "art"

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New scam targeting women: 9 out of 10 girls fall for it—be sure to tell your daughter! Don’t forget

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New scam targeting women: 9 out of 10 girls fall for it—be sure to tell your daughter! Don’t forget

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