UC Davis #12: exp integrate ∫(27e^(9x) + e^(12x))^(1/3) dx

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

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

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Lamar U: trig integral ∫sin(13z) sin(4z) dz

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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.

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Lamar U: trig integral ∫cos^5(2t) sin^2(2t) dt

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2nd/2ways: count perm Show P(n,n)=P(n,n-1)

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Find the median of 4,6,8,...,296

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Example: Find the sum

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Diff Eq: Solve sec(x) dy/dx=y+sin(x) via Integrating factor [IF]

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Review Add Math: 1.2/parts: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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trig integral ∫sin(x) cos(x) cos(2x) cos(4x) cos(8x) cos(16x) cos(32x) dx

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exp integral e^2x/(1+e^x) dx

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pascal triangle: count comb Show nCk = (n-1)Ck + (n-1)C(k-1)

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2 ways: trig exp derivative e^(sin(x)) sin(e^x)

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2nd/3ways: exp Derivative x^x

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2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))

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2nd way: trig integral ∫(sec(x) tan(x))/(sec^2(x)-sec(x)) dx

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2nd/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via "picture".

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2 ways: diff eq Solve dy/dx=y-1

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trig Prove each identity ... 1) to 10)

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