\[\Large \int\limits_{1}^{2}(x-1)\sqrt{2-x}\space dx\]

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\[\Large \int\limits_{1}^{2}(x-1)\sqrt{2-x}\space dx\]

Mathematics
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im thinking integration by parts ... have you tried that?
wELL, i'M NEW TO INTEGRAL, i KNOW SOME TECHNIQUES BUT NOT COMPETELY CONFIDENT WITH IT. i'M CURRENTLY WORK WITH u-sUBSTITUTION. Sorry about caps.
I don't see how I can use u-substitution for this problem...

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oh ok ... yeah substitution may work but i don't see it right away integration by parts is a technique when you have a product of 2 distinct functions \[\int\limits_{?}^{?} f(x) *g(x) dx\]
the equation is given as: \[\int\limits_{?}^{?} u*dv = uv -\int\limits_{?}^{?}v*du\] where u is f(x) and dv is g(x)
Ok, I'm giving it a try.
I don't think it will work. While I'm attempting to solve it, it's getting uglier.
no it will work but yes it can get uglier in the process ... anyway it takes some getting used to i found how u-substitution will work \[u = 2-x\] \[du = -dx\] \[\rightarrow -\int\limits_{?}^{?}(1-u) \sqrt{u} du = -\int\limits_{?}^{?} \sqrt{u} - u \sqrt{u}\]
Hmm clever! Thanks.
yw

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