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2nd/2ways: count perm Show P(n,2)+P(n,1)=n^2
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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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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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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2nd/3ways: trig integral ∫sec(x) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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2nd way: integral ∫ log √x(x^n) dx
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Logical equivalent involving ... tautology & contradiction
1st/2parts: Linear interpolation (2 given points)
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Derivative: Don't blindly use the Quotient Rule every time you see a quotient
Vandermonde's Identity
STPM Math T Sem.2:
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trig integral a) Show that sin(t) cos(t)=1/2 sin^2(t)+c
3 ways: trig integral 1/(1+cos(x)) dx
2nd/3ways: derivative If f(x)=(x-a)(x-b)(x-c), show f'(x)/f(x)=1/(x-1)+1/(x-b)+1/(x-c)
2 ways: trig integral ∫cos^2(x) dx
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