#4 2022 1st/2 ways: MIT Integration Bee Qualifying Exam

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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

3:30

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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lim x/e^x? as x→∞

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lim x/e^x? as x→∞

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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...

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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...

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prob stat: One sample of n=4 scores has a mean of M=10, &

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prob stat: One sample of n=4 scores has a mean of M=10, &

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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prob stat: 1st/2 parts. One sample has a mean of M=6 &

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prob stat: 1st/2 parts. One sample has a mean of M=6 &

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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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#3 UC Davis integrate ∫3/(4+x^(1/3)) dx via power sub

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#3 UC Davis integrate ∫3/(4+x^(1/3)) dx via power sub

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Variability or spread of a distribution. Whey we need it!

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Variability or spread of a distribution. Whey we need it!

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Rutgers U: Verify using calculus

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Rutgers U: Verify using calculus

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Evaluate these 7 integrals ...

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Evaluate these 7 integrals ...

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NYU: 3 ways ∫(1+ln(x))/x dx

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NYU: 3 ways ∫(1+ln(x))/x 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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When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?

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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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1st/2 ways: integral ∫1/(x(x^n -1)) dx

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1st/2 ways: integral ∫1/(x(x^n -1)) dx

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Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction

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Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction

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2010 Raytheon MATHCOUNTS National Competition

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2010 Raytheon MATHCOUNTS National Competition

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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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NYU: compute ∫ln(x)/x^2 dx

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NYU: compute ∫ln(x)/x^2 dx

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Lamar U 2nd way: evaluate trig integral ∫x sin(x^2) [cos^4(x^2) + 8 cos^2(x^2)-10] dx

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Lamar U 2nd way: evaluate trig integral ∫x sin(x^2) [cos^4(x^2) + 8 cos^2(x^2)-10] dx

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