2nd/3 ways: How many chords can be drawn through 21 points on a circle?

MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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Quickie: 6169^2 - 2331^2?

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

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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

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trig Write each expression as an equivalent algebraic expression involving only x.

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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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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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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1st/3ways: exp Derivative x^x

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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3rd way: rational function integral ∫x^3/√ (1+x^2) dx

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3rd/3ways: trig integral ∫sec(x) dx

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2nd way: Express as partial fractions

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#16 MIT 2022 Integration Bee Qualifying Exam

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A bag contains 5 red balls & 3 green balls. A ball is selected at random &

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Diff Eq: Solve sec(x) dy/dx=y+sin(x) via Integrating factor [IF]

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3rd/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

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If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0

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#5 MIT 2022 Integration Bee Qualifying Exam

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