#2 2023 MIT Integration Bee Qualifying Exam

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∫sech(x) dx.

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2 ways: trig integral cos^2(x) sin^2(x) dx

2:21

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

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

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

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

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Pantun Melayu [Sorong papan tarik papan]

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count quick review: Permutation vs Combination

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If u=a+ib is a complex #, then complex conjugate of u*=a-ib. ...

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If u=a+ib is a complex #, then complex conjugate of u*=a-ib. ...

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Prove that the following inner [scalar] product ...

3:13

Prove that the following inner [scalar] product ...

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Swinburne U 2nd way: e^(-e^x) e^x dx

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Swinburne U 2nd way: e^(-e^x) e^x dx

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

3:33

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

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3rd/3ways: count comb A set with n elements has 2^n subsets

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3rd/3ways: count comb A set with n elements has 2^n subsets

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commutative: ab=ba via "picture"

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commutative: ab=ba via "picture"

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count comb: values nCn, nC(n-1), nC(n-2)

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count comb: values nCn, nC(n-1), nC(n-2)

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Alternate way: inverse trig integral ∫e^(m arc tan(x))/(1+x^2) dx

0:42

Alternate way: inverse trig integral ∫e^(m arc tan(x))/(1+x^2) dx

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alternate way: count sum 1+3+5+ ... +(2n-1)

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alternate way: count sum 1+3+5+ ... +(2n-1)

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0:54

Find the number of subsets of {0,{0},{{0}},{{{0}}}}

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1st/2 ways: Show derivative d(arc sin(x))/dx = 1/√(1-x^2)

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1st/2 ways: Show derivative d(arc sin(x))/dx = 1/√(1-x^2)

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Common log mistake: logb(xy^n) ≠ nlogb(xy)

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Common log mistake: logb(xy^n) ≠ nlogb(xy)

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trig integral ∫sec^7(x) tan^5(x) dx

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trig integral ∫sec^7(x) tan^5(x) dx

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There are 2 lines. One line has 3 points & the other line has 6 points.

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There are 2 lines. One line has 3 points & the other line has 6 points.

4 Views