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1st/2 parts stat: SLR ∑ŷk = ∑yk where k=1,n
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1st way: exp ∫(e^x)/x (1+x log(x)) 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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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx
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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
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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trig Write each expression as an equivalent algebraic expression involving only x.
2nd way: log ln(tan(x))/(sin(x) cos(x)) dx
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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]
Alternate way: Evaluate exp integral ∫1/√(1-e^(2x)) dx
A 2 digit number is equal to the sum of the product of its digits & the sum of its digits.
3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))
U Penn: Show that the following decomposition CANNOT hold ...
2 ways: trig integral ∫cos^3(x) sin^2(x) dx
2nd part: n^2 = (tn - tn-1)^2 where tn = nth triangular number
Show that the function u(x,y)=e^x cos(y) is harmonic in the x-y plane
exp log derivative Know the differences ...