#14 2014 MIT Integration Bee Qualifying Exam

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GPT4: A tweet snippet from Michal Kosinski

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GPT4: A tweet snippet from Michal Kosinski

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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 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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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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2nd/3ways: trig integral ∫sec(x) dx

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2nd/3ways: trig integral ∫sec(x) dx

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Review: Linear form, Quadratic form & Bilinear form

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Review: Linear form, Quadratic form & Bilinear form

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

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

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

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

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

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exp Calculate ∫x^3 3^x dx via IBP

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exp Calculate ∫x^3 3^x dx via IBP

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2 ways: exp derivative a^(logb(cos(px+q))

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2 ways: exp derivative a^(logb(cos(px+q))

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prob stat: The p.d.f of a discrete r.v. Y is given by P(Y=y)=cy^2 for y=0,1,2,3,4.

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prob stat: The p.d.f of a discrete r.v. Y is given by P(Y=y)=cy^2 for y=0,1,2,3,4.

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Let B be the mx1 col. matrix [1/m ... 1/m]'. If A =[a1 ... am] is any row matrix. What is AB?

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Let B be the mx1 col. matrix [1/m ... 1/m]'. If A =[a1 ... am] is any row matrix. What is AB?

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Lamar U: #9 1st way: trig integral ∫sec^2(9x) tan^3(9x) dx

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Lamar U: #9 1st way: trig integral ∫sec^2(9x) tan^3(9x) dx

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

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

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Screen Recording 2024-05-19 at 9.56.54 PM

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Screen Recording 2024-05-19 at 9.56.54 PM

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U Penn: Show that the following decomposition CANNOT hold ...

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U Penn: Show that the following decomposition CANNOT hold ...

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Find the equation of the tangent line to the curve x^3-3y^3+xy+21=0 at the point (1,2)

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Find the equation of the tangent line to the curve x^3-3y^3+xy+21=0 at the point (1,2)

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prob stat It is known that P(X)=1/2 & P(Y)=1/4. Given that X & Y are mutually exclusive, find

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prob stat It is known that P(X)=1/2 & P(Y)=1/4. Given that X & Y are mutually exclusive, find

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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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