UC Davis #22: trig integral ∫sin(x) cos(x) e^sin(x) dx

kimetsu no yaiba #kimetsu no yaiba

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

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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

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1st/2parts 3 ways: tn-1 + tn = n^2 where tn = nth triangular number

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log sq root integral ∫ln(√ x^3)/√ √ x dx

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2 ways: trig integral ∫cos^2(x) dx

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Bijection of elements in tn & a pair of elements of (n+1)

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Alternate way: trig integral ∫cos(x) dx

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4 ways: sum Find the sum of the values of 4+3i for i=1,2,...,100

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2 ways: Derivative √ (1+√ (1+√ x)))

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2nd/3part: Maclaurin Series [ahp kia]

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3rd/3ways: trig integral ∫sec(x) dx

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exp log derivative Know the differences ...

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

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