review: When to use ... Sum of A.P n/2(a+l) vs n/2(2a+(n-1)d)

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#10 2023 MIT Integration Bee Qualifying Exam

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#10 2023 MIT Integration Bee Qualifying Exam

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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.

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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(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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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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

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

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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2nd way: integral ∫ log √x(x^n) dx

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2nd way: integral ∫ log √x(x^n) dx

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(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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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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

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

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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx

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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx

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Find the 2nd-order partial derivatives of f(x,y)=2xy^2-3x^2+xy^3

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Find the 2nd-order partial derivatives of f(x,y)=2xy^2-3x^2+xy^3

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partial Let f(x,y,z)=x e^(yz). Compute fxzy & fyxz.

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partial Let f(x,y,z)=x e^(yz). Compute fxzy & fyxz.

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prob stat a) Calculate the mean & the std deviation of 4 numbers 2,3,6,9

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prob stat a) Calculate the mean & the std deviation of 4 numbers 2,3,6,9

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

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2nd way: trig integral ∫ √sec^5(x)/√sin^3(x) dx

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2nd way: trig integral ∫ √sec^5(x)/√sin^3(x) dx

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2nd way: sq rt integral ∫(√x)/(x+1) dx

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2nd way: sq rt integral ∫(√x)/(x+1) dx

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2 ways: trig integral cos^2(x) sin^2(x) dx

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2 ways: trig integral cos^2(x) sin^2(x) dx

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Screen Recording 2023-12-07 at 2.04.49 AM

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Screen Recording 2023-12-07 at 2.04.49 AM

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