#12 2014 MIT Integration Bee Qualifying Exam

Peter Pan (by J. M. Barrie) - Read by Philip Franks (Michael Jayston as Captain

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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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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Swinburne U 2nd way: e^(-e^x) e^x dx

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Pantun Melayu [Sorong papan tarik papan]

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Large sq made up of 100 smaller unit sq. Border of the large sq are colored red. WithOUT counting ..

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Show log b^n(x^m) = m/n logb(x)

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commutative: ab=ba via "picture"

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review: prob stat Population variance vs sample variance

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hyper trig integral ∫cosh(x) a^(logb(sinh(x)) ))dx

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Careful: arc sin(sin(5π/4)) ≠ ...

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exp derivative x^n w.r.t x

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2nd way: integral ∫x^2 √(x^3+1) dx vs ∫x^3 √(x^3+1) dx

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"baby" fact: exp e^(ix)

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trig integral ∫1/(1+cos(ax+b)) dx

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UC Davis #6: ∫ (2+tan(x))^2 dx

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derivative y=a^(arc sin(x))^2

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