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2nd/3 parts: Growing patterns
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
9 Views
2nd way: integral ∫ log √x(x^n) dx
35 Views
MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
12 Views
CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
1st/3 parts: Growing patterns
2nd/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via "picture".
1st/3parts: Mean of 1,2,3,...,n SAME as Mean 1,n
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3 ways: rational function integral ∫(x^2+1)/(x-1)^3 dx
2nd part: n^2 = (tn - tn-1)^2 where tn = nth triangular number
integral ∫x dx withOUT using power rule
1st/2ways: r-Permutations
Lamar U: trig integral ∫cos^5(2t) sin^2(2t) dt
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Evaluate trig integral ∫1/(a+bcos^2(x)) dx
1st/2ways: logic Import-Export
2 ways: trig integral ∫ sin(ax+b) dx
5th/10parts: Material implication
1st way: Differentiate the function w.r.t x log10(x)+logx(10)+logx(x)+log10(10)
Florida International U: Find derivatives ...defined implicitly ... (a)-(c)