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1st/2ways: 1+2+3+...+(n-1)+n+(n-1)+...+3+2+1 = n^2
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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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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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2nd way: integral ∫ log √x(x^n) dx
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2 ways: derivative ln(ax-b)^(p-qx)
trig integral ∫7x sin(x^2) sin(4x^2) dx
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2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS
2 ways: integral (3+5x)/(x(x-1)) dx
Let f(x,y)=4-2xx^2-y^2. Find the slope of the tangent line at the point (1,1,1) on the curve formed
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Express the sum of the digits of the number (1000^20 - 20) in decimal notation
A 2 digit number is equal to the sum of the product of its digits & the sum of its digits.
2 ways: ∫ 1/(10x^2 -x-21) dx
Review: trig sin(x+90)= cos(x) & cos(x+90)=-sin(x)
2nd/2parts example Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n
3 ways: exp integral e^(2x)/(1+e^x) dx