#2 2023 MIT Integration Bee Qualifying Exam

MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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2nd way: trig integral ∫1/(cos^2(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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logic: tautology (¬p→q)∧(¬p→¬q) →p

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

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Pantun Melayu [Sorong papan tarik papan]

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

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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

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Find the equation of the tangent line to the curve x^3-3y^3+xy+21=0 at the point (1,2)

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1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

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1st/2ways: r-Permutations

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2 ways: derivative a^f(g(x))

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logic: contradiction p∧¬p

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Screen Recording 2024-02-16 at 8.23.14 PM

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Giant ships are launched in different countries: Japan uses a push-to-launch method, while India’s m

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Evaluate the integrals

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3rd/10parts: Exclusive disjunction

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2 ways: integral ∫(x-a)/(x+a) dx

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trig integral ∫sin(x) cos(x) cos(2x) cos(4x) cos(8x) cos(16x) cos(32x) dx

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