#11 2014 MIT Integration Bee Qualifying Exam

sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))

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

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

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Review: Arithmetic Series a+(a+d)+(a+2d)+...+(a+(n-1)d)=

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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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5 ways: trig Derivative of sin^2(x)

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2 ways: trig integral ∫tan^3(x) sec^2(x) dx

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Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction

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trig integral ∫tan^n(x) dx where n is EVEN via Reduction formula

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NUS MA1102R: Find ALL second-order partial derivatives of f(x,y) = x^2 y -y^3 + ln(x)

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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]

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Columbia U: 6th/6 ways Evaluate the indefinite integral ∫1/(1+e^x) dx

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trig integral ∫x sec^5(x^2) tan(x^2) dx

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Which of the following data sets has a median of 3?

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Think about the SS values you might obtain if you computed SS for these 22 samples...

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3 ways: Derivative x^(-1/x)

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Simplify the Boolean function F=A+A'B

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2nd way: integral ∫x^2/(x^3 -2)^5 dx

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NYU: 2nd way compute integral ∫x(1+x^2) dx

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A couple has 6 children whose ages are 6,8,10,12,14,16. Find the variance in ages.

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