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exp Calculate ∫x^3 3^x dx via IBP
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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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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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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logic Idempotent law show x=xVx
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Swinburne U 2nd way: e^(-e^x) e^x dx
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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Review: Linear form, Quadratic form & Bilinear form
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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable
prob stat: The p.d.f of a discrete r.v. Y is given by P(Y=y)=cy^2 for y=0,1,2,3,4.
Variability or spread of a distribution. Whey we need it!
IIT-1995 2nd way integral ∫x^5/(1+x^3) dx
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2 way: exp integral e^(ax+b)/1+e^(ax+b)) dx
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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3rd/3 ways: Alternate way: Given 2 points, find equation of st line passing the ..
When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?
Lamar U: trig integral ∫cos^5(2t) sin^2(2t) dt
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2nd way: sq rt integral ∫(√x)/(x+1) dx