A couple has 6 children whose ages are 6,8,10,12,14,16. Find the variance in ages.

RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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Lamar U 2nd way: evaluate integral ∫√(1+2ln(7x))/2 +10x^3/(x^4 +9) dx

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Lamar U: Assume that x=x(t) & y=y(t) & differentiate the following equation wrt t

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#8 2021 MIT Integration Bee Qualifying Exam

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Evaluate the integrals

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Lamar U: #11 trig integral ∫csc^6(x/4) cot^4(x/4) dx

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trig integral ∫tan^n(x) dx where n is EVEN via Reduction formula

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2nd way: trig integral ∫1/(a+b sin(x)+c cos(x)) dx

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AP Calculus 4th way: exp ∫1/(1+e^x) dx via 3rd u-sub

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2nd way: integral ∫x/(2ax-x^2) dx

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UC Davis #3 2nd way: ∫(2-x)/(x^2+5x)dx [integration by partial fraction]

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Derivative d(x^(arc sin(x))/d(arc sin(x))

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AP Calculus 2nd way: integral ∫ (3^(x+1)-7^(x-1))/21^x dx

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2 ways: derivative √(x+1) √(x-1)

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5 ways: integral ∫a^(px+q) dx

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China's top ten strange cases: the deceased had a key in his mouth and a talisman wrapped around his

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Soy sauce latte, a stupid move or a smart one?

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