1st/2ways: 1+2+3+...+(n-1)+n+(n-1)+...+3+2+1 = n^2

2nd way: integral ∫ log √x(x^n) dx

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Novice's Journey to Immortality - Mei Ning Character Song

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

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

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

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

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

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exp integral e^2x/(1+e^x) dx

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prob stat: The discrete r.v. W has prob dist. as shown

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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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Show that ar sinh(x) = ln(x + √ (x^2+1))

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Screen Recording 2024-05-05 at 11.28.23 PM

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A bag contains 20 identical red marbles, 20 identical green marbles, & 20 identical blue marbles.

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Why the mean of AP is the median of AP? mean=median?

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review: When to use ... Sum of A.P n/2(a+l) vs n/2(2a+(n-1)d)

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integration bee 2014 UNSW 3rd way: e^x(cos(x)+sin(x)) dx

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Review: Arithmetic Series a+(a+d)+(a+2d)+...+(a+(n-1)d)=

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Let f(x) be a polynomial of degree 1. If f(10)-f(5)=15, then f(20)-f(5)=?

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prob stat: A group consists of 4 girls & 7 boys. In how many ways can a team of 5 members ...

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Screen Recording 2024-05-11 at 8.58.53 PM

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