Differentiate and then Integrate

[david.ko3]

Hi!
There is this question when it asks me to differentiate and then integrate. It is differentiated by product rule however i have no clue how to integrate the original function. Help is very much appreciated!

Sorry the Question was:
Differentiate xsinx and then find the integral (pi/3 to 0) xcosx dx.

Mod edit: merged double post. Please use the 'modify' button on the bottom of your post next time -- Calebark

[RuiAce]

\[ \text{You have computed that}\\ \frac{d}{dx} x\sin x = \sin x + x \cos x. \]

(The formal wording is that they're inverse operations, but I'm not focusing on 3U terminology in the 2U thread.)
\[ \text{That illustrates the basic idea, but note that you can split the LHS into}\\ \int \sin x \,dx + \int x \cos x\,dx.\\ \text{Also note that you are currently dealing with definite integrals, so use boundaries instead of }+C.\]
Reply further if you have more troubles.

[david.ko3]

Oh Ok! Thanks Very much!!! Helped me heaps!!