UC Davis #22 [THE INTEGRATION OF RATIONAL FUNCTIONS] withOUT u-sub

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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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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logic Idempotent law show x=xVx

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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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Solve the differential equation cos^2(y) dx +(1+e^(-x) sin(y) dy=0

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

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UC Davis #14: integral ∫x √(4-x) 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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Lamar U 2nd way: evaluate exp integral ∫e^(2x)/(1+e^(2x)) 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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A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R

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

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1st/2 ways: MIT Integration Bee

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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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