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

UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n

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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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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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Review: Linear form, Quadratic form & Bilinear form

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

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🪔 Happy Deepavali 🪔 [Nov-12-2023]

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Swinburne U 2nd way: e^(-e^x) e^x dx

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1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+sin^2(x)) dx

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stat: SLR Properties of residuals

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2 way: exp integral e^(ax+b)/1+e^(ax+b)) dx

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#12 2024 1st/2ways: MIT Integration Bee Qualifying Exam

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The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.

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A cubical die, numbered 1 to 6 is weighted so that a six is twice as likely to occur as any other #.

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Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5

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prob stat: The speeds, to the nearest mile per hour,, of 120 vehicles passing a check point

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A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R

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prob stat: The following frequency table gives the values obtained

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Express the sum of the digits of the number (1000^20 - 20) in decimal notation

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Inazuma Elven Go Galaxy! (Episode 1)

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2nd way: integral sec^2(x) csc^2(x) dx

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