#17 2022 MIT Integration Bee Qualifying Exam

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IIT-1995 2nd way integral ∫x^5/(1+x^3) dx

2:16

IIT-1995 2nd way integral ∫x^5/(1+x^3) dx

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5 ways: integral ∫a^(px+q) dx

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5 ways: integral ∫a^(px+q) dx

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2nd way: ∫1/(√(x-α)(x-β)) dx

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2nd way: ∫1/(√(x-α)(x-β)) dx

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Let f(x,y)=4-2xx^2-y^2. Find the slope of the tangent line at the point (1,1,1) on the curve formed

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Let f(x,y)=4-2xx^2-y^2. Find the slope of the tangent line at the point (1,1,1) on the curve formed

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2 ways: ∫1/(x^2+2x-3) dx

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2 ways: ∫1/(x^2+2x-3) 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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A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R

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If u=f(y/x) then prove that x∂u/∂x + y∂u/∂y = 0

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If u=f(y/x) then prove that x∂u/∂x + y∂u/∂y = 0

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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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derivative y=f(logb(arc tan(px+q))

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derivative y=f(logb(arc tan(px+q))

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2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS

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2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS

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#22 2019 MIT Integration Bee Final

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#22 2019 MIT Integration Bee Final

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2nd way: derivative ∫log (f(x))^g(x) (p(x))^r(x)

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2nd way: derivative ∫log (f(x))^g(x) (p(x))^r(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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U Penn: Evaluate trig integral ∫(sin^2(x) -cos^2(x))/(sin(x)-cos(x))^2 dx

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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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2010 Raytheon MATHCOUNTS National Competition

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2010 Raytheon MATHCOUNTS National Competition

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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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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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Show log b^n(x^m) = m/n logb(x)

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Show log b^n(x^m) = m/n logb(x)

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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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2nd way: derivative (x^x)√ x

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2nd way: derivative (x^x)√ x

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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]

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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]

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