#10 2023 MIT Integration Bee Qualifying Exam

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1 View PremiumNov 27, 2023

∫ ((1-x)^3 +(x-x^2)^3+(x^2-1)^3-3(1-x)(x-x^2)(x^2-1)) dx.

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A cubical die, numbered 1 to 6 is weighted so that a six is twice as likely to occur as any other #.

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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0:53

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

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

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2nd/3ways: trig integral ∫sec(x) dx

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Calculus: If u=f(x+cy)+g(x-cy) then uxx / uyy ?

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2 ways: Derivative √ (1+√ (1+√ x)))

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2nd/2 ways: Alternate way: Given 2 points, find equation of st line passing the ..

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1:08

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4 ways: trig integral ∫sin(x) cos(x) dx

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2:41

COMMON MISTAKE!: exp derivative d/dx(a^x) ≠ x a^(x-1)

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3rd/3ways: exp Derivative x^x

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2 ways: exp integral p^(qx+r) dx

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2:07

Cancellation Law ❌ Matrices

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Alternate way: Derivative y=ln((x^4-8)^5/(x^6+5x)cos(x))

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2 ways: log derivative log3(x)

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trig integral ∫sin^2(x)/cos^6(x)) dx

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exp derivative e^f(g(x)) h(x)

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