2 ways: trig Show (1-cos(x))/sin(x)=sin(x)/(1+cos(x))

#16 MIT 2022 Integration Bee Qualifying Exam

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🪔 Happy Deepavali 🪔 [Nov-12-2023]

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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2nd way: integral ∫ log √x(x^n) dx

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Review Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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trig Evaluate each expression below withOUT using a calculator.

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Derivative: Don't blindly use the Quotient Rule every time you see a quotient

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integral ∫(8x+12) (x^2+3x+1)^4 dx vs integral ∫(8x+12)/(x^2+3x+1)^4

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Review Add Math: 1.1/parts: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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trig integral ∫1/(cos^2(a+bx) √(p^2-qtan(a+bx)) )dx

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sq root 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫1/(√x (1+√x))dx

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Screen Recording 2024-05-19 at 11.13.23 PM

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2nd way: sq root integral ∫1/(1+ √'x) dx

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2nd way: trig integral ∫(sec(x) tan(x))/(sec^2(x)-sec(x)) dx

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2nd way: trig integral ∫ √sec^5(x)/√sin^3(x) dx

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trig Prove each identity ... 1) to 10)

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2 ways: trig Prove the identity sin(2x)=2/(tan(x)+cot(x))

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2nd way: trig integral ∫ tan(x)/(tan^2(x)+tan(x)+1) dx

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3 ways: trig integral 1/(1+cos(x)) dx

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