#11 2014 MIT Integration Bee Qualifying Exam

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0 วิว Premium30/11/2023

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

1:11

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

5 วิว

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

1:23

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

11 วิว

alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

8:49

alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

4 วิว

prpob stat A bag contains 5 black balls 6 red balls. Determine the number of ways in which ...

1:06

prpob stat A bag contains 5 black balls 6 red balls. Determine the number of ways in which ...

1 วิว

1st way: exp ∫(e^x)/x (1+x log(x)) dx

1:49

1st way: exp ∫(e^x)/x (1+x log(x)) dx

22 วิว

Pantun Melayu [Buah cempedak di luar pagar]

0:28

Pantun Melayu [Buah cempedak di luar pagar]

19 วิว

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

5:18

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

23 วิว

U North Texas Integration Bee 2nd way: x^2/√(x-1) dx

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U North Texas Integration Bee 2nd way: x^2/√(x-1) dx

1 วิว

Do you know ... in tagalog?

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Do you know ... in tagalog?

2 วิว

MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

17 วิว

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

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

23 วิว

2nd way: integral ∫ log √x(x^n) dx

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2nd way: integral ∫ log √x(x^n) dx

65 วิว

2 ways: exp integral ∫e^√x dx

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2 ways: exp integral ∫e^√x dx

0 วิว

2nd way: derivative (x/a)^n/(n-1) + (y/b)^n/(n-1) = 1

2:07

2nd way: derivative (x/a)^n/(n-1) + (y/b)^n/(n-1) = 1

0 วิว

inverse trig integral ∫x arc sec(x^2)/(x^2 √(x^2-1)) dx

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inverse trig integral ∫x arc sec(x^2)/(x^2 √(x^2-1)) dx

0 วิว

trig integral ∫arc sin(x)/√(1-x^2) dx vs ∫1/(arc sin(x) √(1-x^2)) dx

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trig integral ∫arc sin(x)/√(1-x^2) dx vs ∫1/(arc sin(x) √(1-x^2)) dx

0 วิว

Any function f is a sum of an EVEN & an ODD function

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Any function f is a sum of an EVEN & an ODD function

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2 ways: trig integral ∫ sin^2(ax+b) dx

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2 ways: trig integral ∫ sin^2(ax+b) dx

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2nd way: trig integral ∫sin(x/a) dx

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2nd way: trig integral ∫sin(x/a) dx

0 วิว

2nd way: integral ∫1/x log mb(x) dx

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2nd way: integral ∫1/x log mb(x) dx

0 วิว