Screen Recording 2024-02-22 at 10.23.21 PM

2024 #3 MIT Integration Bee Final Lightning Round

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

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) 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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Review: Linear form, Quadratic form & Bilinear form

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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example: Mean, Median & Mode

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2nd way: ∫(x+3)/(x^2+6x)^2 dx vs ∫(x+3)(x^2+6x)^2 dx

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prob stat: For the sample shown in the freq distribution table, what is the mode?

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3 ways: Find 1+2+3+ ... + n^2.

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integral sin(x)/(1+sin(x)) dx

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A bag contains 5 red balls & 3 green balls. A ball is selected at random &

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Consider the mode, median, mean.

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1st/10 parts: Logical disjunction

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2nd way: integral ∫1/√(arc sin(a)x - √√b) dx Calculus

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Find dy/dx where x^y+y^x=1

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sq root 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫1/(√x (1+√x))dx

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prob stat: One sample of n=4 scores has a mean of M=10, &

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