## AmTran_Bus one year ago Is the LIATE rule for integration by parts correct?

1. SolomonZelman

Yes, that is the order

2. SolomonZelman

of choosing a function to differentiate

3. AmTran_Bus

Does it always go? I'm a little hard to believe it always works.

4. SolomonZelman

Well, it is a suggestion for user that don't know intuitively - to tell them which function should they diffeentiate. It is not a "rule" literally, as the "chain rule" - not to that extent a "rule".

5. SolomonZelman

6. SolomonZelman

I mean if you want: $${\displaystyle \int} wx~dx=(\int w)\cdot(x)-{\displaystyle \int} (\int w)\cdot(x)'dx$$ $${\displaystyle \int} wx~dx=( wx)\cdot(x)-{\displaystyle \int} (wx)\cdot(1)dx~+C$$ by parts - comes from product rule, thus should have +C (because it comes from INTEGRATING both sides of the product of the deriavtive) $${\displaystyle \int} wx~dx=( wx)\cdot(x)-{\displaystyle \int} wx~dx~+C$$ $$2{\displaystyle \int} wx~dx=( wx)\cdot(x)~+C$$ $$\displaystyle \int wx~dx=\frac{w}{2}x^2~+\frac{C}{2}$$ $$\displaystyle \int wx~dx=\frac{w}{2}x^2~+C$$

7. SolomonZelman

i did by parts on a wx (with respect to x)

8. AmTran_Bus

Wow super nice.

9. SolomonZelman

tnx,n,yw O~O

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