## geerky42 2 years ago $\Large \int\limits_{1}^{2}(x-1)\sqrt{2-x}\space dx$

1. dumbcow

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

2. geerky42

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.

3. geerky42

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

4. dumbcow

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

5. dumbcow

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

6. geerky42

Ok, I'm giving it a try.

7. geerky42

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

8. dumbcow

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

9. geerky42

Hmm clever! Thanks.

10. dumbcow

yw