Question

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

Answer 1

im thinking integration by parts ... have you tried that?

Answer 2

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.

Answer 3

I don't see how I can use u-substitution for this problem...

Answer 4

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
\[\int\limits_{?}^{?} f(x) *g(x) dx\]

Answer 5

the equation is given as:
\[\int\limits_{?}^{?} u*dv = uv -\int\limits_{?}^{?}v*du\]
where u is f(x) and dv is g(x)

Answer 6

Ok, I'm giving it a try.

Answer 7

I don't think it will work. While I'm attempting to solve it, it's getting uglier.

Answer 8

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
\[u = 2-x\]
\[du = -dx\]
\[\rightarrow -\int\limits_{?}^{?}(1-u) \sqrt{u} du = -\int\limits_{?}^{?} \sqrt{u} - u \sqrt{u}\]

Answer 9

Hmm clever! Thanks.

Answer 10

yw