sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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workpoint film

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Let f(x) be a polynomial of degree 1. If f(10)-f(5)=15, then f(20)-f(5)=?

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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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Do you know ... in tagalog?

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Pantun Melayu [Buah cempedak di luar pagar]

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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prpob stat A bag contains 5 black balls 6 red balls. Determine the number of ways in which ...

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2nd way: integral ∫ log √x(x^n) dx

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U North Texas Integration Bee 2nd way: x^2/√(x-1) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(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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2nd way: derivative (a-bx)^(px-q)

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UC Davis #14: trig integral ∫(sin(x)-cos(x))(sin(x)+cos(x))^5 dx

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UC Davis #9: trig integral ∫cos^2(x)/(1+sin(x)) dx

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UC Davis #18: trig integral ∫sec(x) tan(x) √(4+3sec(x)) dx

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UC Davis #22: trig integral ∫sin(x) cos(x) e^sin(x) dx

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2nd way: sq root integral ∫1/(1+ √'x) dx

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UT Austin: 2 ways trig integral ∫sin(2x+1)/cos^2(2x+1) dx

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prob stat: 2 formula for sample variance

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3rd/3 ways: trig integral ∫ sin(ax+b) dx

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