1) integral ∫1/5 dx/(1+x) vs 2) integral ∫sec^(5x)/(1+ tan(5x)) dx

#4 2017 MIT Integration Bee Qualifying Exam

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2nd way: integral ∫ log √x(x^n) dx

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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2 ways: sq root derivative 1/(√√(1/√x))

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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derivative Find d2y/dx2 for this function y=ln(x)/(1-x)

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The prob. density function of a r.v X is given by the formula

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Lamar U 2nd way: evaluate exp integral ∫e^(8x)(4+e^(4x))^(-3) dx

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When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?

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Find the expected value & the variance of a geometric r.v. X

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U Penn: Evaluate trig integral ∫(sin^2(x) -cos^2(x))/(sin(x)-cos(x))^2 dx

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prob stat: The following frequency table gives the values obtained

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UC Davis: #11 exp trig ∫cos(5x)/e^sin(5x) dx

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2nd way: integral 1) ∫1/√(a - √b x^2)dx vs 2) ∫1/√(a - √b x^2) dx

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#1 2017 MIT Integration Bee Qualifying Exam

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1st/2 way: Expand e^sin(x) by Maclaurin's Theorem

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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#3 2017 MIT Integration Bee Qualifying Exam

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AP Calculus: 2nd way integral log √√x (x) dx

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NONelementary integral ∫e^(ax)/x dx

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