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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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U North Texas Integration Bee 2nd way: x^2/√(x-1) dx
Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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2nd way: integral ∫ log √x(x^n) dx
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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"
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Pantun Melayu [Buah cempedak di luar pagar]
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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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2nd way: derivative x^n w.r.t. n^x
log integral ∫(ln(x))^m/x dx
integral ∫x^3/(1-x^8) dx
trig integral ∫1/(4-3cos^2(x)+5sin^2(x)) dx
1st/2ways: trig integral cos(2x)/(cos^2(x) sin^2(x)) dx
trig derivative differentiate x^sin(x) + (sin(x))^cos(x)
5th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number