Screen Recording 2024-05-19 at 11.13.23 PM

Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5

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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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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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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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Screen Recording 2024-02-16 at 8.23.14 PM

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2010 #2 MIT Integration Bee

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JHU: integral ∫t^3 e^(t^2) dt

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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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Screen Recording 2024-02-21 at 11.48.01 PM

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Screen Recording 2024-02-22 at 10.45.08 PM

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Screen Recording 2024-02-16 at 9.12.26 PM

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happy deepavali 2025 fireworks 🎇

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Columbia U: 2nd way integral Find ∫1/(x √(9-x^2)) dx withOUT trig-sub

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JHU: sq root integral ∫e^√x dx

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prob stat a) Calculate the mean & the std deviation of 4 numbers 2,3,6,9

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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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