course mth 272 I found this assignment difficult.
......!!!!!!!!...................................Applied Calculus II
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17:09:25
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**** Query problem 6.1.5 (was 6.1.4) integral of (2t-1)/(t^2-t+2)
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17:09:47 ln (t^2-t+2) + C
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17:09:48
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**** What is your result?
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17:10:00 ln ( t^2-t+2) + C
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17:10:01
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**** What substitution did you use and what was the integral after substitution?
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17:10:41 general log rule: (du/dx) / u dx = 1/u = ln (u) + C
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17:10:42
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**** Query problem 6.1.13 (was 6.1.32) integral of 1 / (`sqrt(x) + 1)
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17:10:57 2 (x+1)^(1/2) + C
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17:10:59
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**** What is your result?
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17:11:15 2 ( x+1) ^ (1/2) + C
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17:11:16
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**** What substitution did you use and what was the integral after substitution?
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17:13:54 general power rule: u^n+1 / n+1 + C
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17:13:55
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**** If you let u = `sqrt(x) + 1 then what is du and, in terms of u, what is x?
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17:15:57 du = 1 x = u^2-1
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17:15:58
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**** If you solve du = 1 / (2 `sqrt(x)) dx for dx, then substitute your expression for x in terms of u, what do you finally get for dx?
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17:18:29 dx = du( 2 sqrt (x) and u*2-1 = x so u^2-1 - du(2 sprt (x)) = dx
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17:18:30
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**** What therefore will be your integrand in terms of u and what will be your result, in terms of u?
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17:20:11 u = sqrt.(du(2sprt(x)) dx -1)
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17:20:12
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**** What do you get when you substitute `sqrt(x) + 1 for u into this final expression?
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17:21:02 x= du(2sqt (x) dx - 2
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17:21:03
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**** query problem 6.1.56 (was 6.1.46) area bounded by x (1-x)^(1/3) and y = 0
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17:29:19 u = (1-x) ^ (1/3) u^3= 1-x x= 1-u^3 dx=-3u^2du not sure what to do next or if identifying these is how to start.
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17:29:20
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**** What is the area?
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17:29:25 ??
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17:29:26
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**** What integral did you evaluate to obtain the area?
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17:29:30 ??
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17:29:31
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**** What substitution did you use to evaluate the integral?
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17:29:35 ??
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17:29:35
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**** Query problem 6.1.64 P = int(1155/32 x^3(1-x)^(3/2), x, a, b).
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17:50:28 from 0 to 25: found 1155/32 (1-u^2/3) (u) (-2/3 ^-.33) du between 1 and .91 but from the example in the book i still am not clear how to solve
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17:50:28
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**** What is the probability that a sample will contain between 0% and 25% iron?
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17:50:44 solve the long expression to get the probability
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17:50:45
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**** What is the probability that a sample will contain between 50% and 100% iron?
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17:51:01 use other limits with the same expression and solve
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17:51:01
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**** What substitution or substitutions did you use to perform the integration?
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17:51:39 constant rule and simple power rule
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17:51:39
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**** Query Add comments on any surprises or insights you experienced as a result of this assignment.
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17:52:56 this material seems a bit difficult the way they explained in the textbook. other than that, in integration by substitution, it seems like you have to memorize the basic formulas and in turn recognize how to use them.
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