#15 MIT 2022 Integration Bee Qualifying Exam

1st/3ways: exp Derivative x^x

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

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Pantun Melayu [Buah cempedak di luar pagar]

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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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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(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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3 picture views of the sum ... 1+2+3+...+n

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exp integral e^2x/(1+e^x) dx

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Example: Find the sum

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2nd example: Find the sum -0.31, -0.19, -0.07, 0.05, 0.17, 0.29 via median

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expon directive a^f(x)

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1st/3part: Maclaurin Series [ahp kia]

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Diff Equ: Solve y-xdy/dx=b(1+x^2dy/dx)) via integrating factor [IF]

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6th form Pure Math: Evaluate the integrals

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ROLL.OVER.AND.DIE.S01E05 [Hindi-English-Japanese]

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3rd/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

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4th way: rational function integral ∫x^3/√ (1+x^2) dx

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Review: trig tan(x+360)= tan(x) & tan(x+180)=tan(x)

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2nd/3part: Maclaurin Series [ahp kia]

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Review Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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