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anonymous
 5 years ago
Anyone want to help with the integral of x/(x+2)^1/2 from 1 to 2?
anonymous
 5 years ago
Anyone want to help with the integral of x/(x+2)^1/2 from 1 to 2?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I just don't know how to set it up, what should u be?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0say u = 1/(sqrt(x2) then you have integral of u/u^22. use partial fractions to solve.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry,u = 1/sqrt(x+2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lemme know how it works out.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok thx I'll try it out

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0did you get du=1/2(x+2)^3/2? or did I do something wrong

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats right, just checked it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok great! . i'd actually not done it. I just looked at the problem and did some calculation in my head. sorry.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0np, wait though not done yet

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so next du=1(x+2)/2(x+2)^1/2 right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0umm, you can solve it entirely in u and plug in the values of u, since this is a definite integral.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no need to deal with x at all

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait how come? I thought we had to make du look like the remaining terms in the integral, sorry I've just learned integrals today

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay. let me get back to you with this. I will take out my pen and paper and write it down. Do ask someone else too.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, so first Let \(u = (x+2)^{1/2} \implies du = (1/2)(x+2)^{1/2}dx\) \[ \implies dx = 2(x+2)^{1/2} du\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So then \[\int_{1}^2\frac{x}{(x+2)^{1/2}}dx = \int_1^2[u^22]du\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wow, ok let me try that out thanks, do u know of any rules to find these? or to you just have to guess the u sometimes?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and does the integral change from 1 to 2, to 1 to 2, or is that a typo?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The integral changes because \(u = (x+2)^{1/2}\) so when x = 1, u = 1 and when x = 2, u = 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right right, forgot about that, when you said you forgot the 2, is it ]2u^22]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ah right, that would make more sense, well thx again

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you see how I arrived at \(2[u^22]\)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Cause I kinda skipped some steps there.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well no, but I understand that it's the right equation to the integral

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can show the steps.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0there are steps to it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since \( u = (x+2)^{1/2} \implies x = u^2 2\) \(\implies dx = 2u\ du\) \[\implies \frac{x}{(x+2)^{1/2}}dx = \frac{u^22}{u} *2u\ du\] \[=2[u^22]\ du\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0awesome thanks a lot, I don't think we even learned that yet

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you always implicitly differentiate x? (x'=dx and not 1?)
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