Suppose E & F are 2 complementary events. Must E & F be mutually exclusive? Explain your answer.

integral ∫(8x+12) (x^2+3x+1)^4 dx vs integral ∫(8x+12)/(x^2+3x+1)^4

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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

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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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Lamar U 2nd way: evaluate exp integral ∫e^(2x)/(1+e^(2x)) dx

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

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

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Amaya & Ben integrated (1+x)^2 wrt x using different methods as follows ...

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Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx

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prob stat: The following frequency table gives the values obtained

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NUS MA1102R: Find ALL second-order partial derivatives of f(x,y) = x^2 y -y^3 + ln(x)

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If pv^a=C (where a & C are constant) find dv/dp & d2v/dp2

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Lamar U Calculus: #14 integral ∫ [9sin^5(3x)-2cos^3(3x)] csc^4(3x) dx

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Screen Recording 2024-02-16 at 9.14.39 PM

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