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

1. dumbcow Group Title

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

2. geerky42 Group Title

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 Group Title

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

4. dumbcow Group Title

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 Group Title

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 Group Title

Ok, I'm giving it a try.

7. geerky42 Group Title

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

8. dumbcow Group Title

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 Group Title

Hmm clever! Thanks.

10. dumbcow Group Title

yw