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2010 #2 MIT Integration Bee
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(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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example: Mean, Median & Mode
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4 ways: trig integral ∫tan(x) dx
NUS MA1102R: For f(x,y) = e^(xy) + x/y, compute fx & fy
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NUS MA1102R: Find ALL second-order partial derivatives of f(x,y) = x^2 y -y^3 + ln(x)
Is 4cos^3(x)-3cos(x) EVEN, ODD, NEITHER, BOTH EVEN & ODD?
integral ∫x^3/(x+2) dx
A bag contains 5 red balls & 3 green balls. A ball is selected at random &
#6 2010 MIT Integration Bee Qualifying Exam
alternate way: count sum 1+2+3+ ... +n
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derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2 - xy1 = a^2y.
sq root 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫1/(√x (1+√x))dx
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Any function f is a sum of an EVEN & an ODD function
Review count Common mistake Rearrangement LOOT=4!/2 vs LULL NOT = 4!/3
Which 3 are functions? Why the other 2 NOT?