## amyna one year ago find intergal: this is an interrogation by parts problem

1. amyna

|dw:1441854137872:dw|

2. amyna

i got: u=x^3 du=3x^2 dv=e^-x^2 v= i don't know lol

3. freckles

$u=x^2 \\ du=2x dx \\ \text{ now multiply both sides of } du=2x dx \text{ by } \frac{1}{2}x^2 \\ \text{ so we have } \\ \frac{1}{2}x^2 du=x^3 dx \\ \text{ but recall } x^2=u \\ \text{ so we have } \frac{1}{2}u du=x^3 dx$ once I make this substitution then I would do integration by parts

4. freckles

or you could have actually went with the sub u=-x^2 instead

5. amyna

ok i'll try and do this, and see what i get. thanks!

6. amyna

ya i don't know what I'm doing! can i use integration by parts first?

7. anonymous

this is an interrogation huh? ;)

8. zepdrix

buhaha XD

9. freckles

you could try integration by parts but as you wrote earlier it is a little confusing to do a substitution would make the integration by parts less confusing -- what do you mean you don't know what you are doing? like you couldn't do the substitution I gave you above ?

10. amyna

ya where did you get the x^3 from?

11. freckles

$\int\limits x^3 e^{-x^2} dx \\ \text{ replace } x^2 \text{ with } u \\ \text{ replace } x^3 dx \text{ with } \frac{1}{2} u du \\ \text{ giving you } \\ \int\limits \frac{1}{2} u e^{-u} du$

12. freckles

did you read the third line ?

13. freckles

$u=x^2 \\ du=2x dx \\ \text{ now multiply both sides of } du=2x dx \text{ by } \frac{1}{2}x^2 \\ \text{ so we have } \\ \frac{1}{2}x^2 du=x^3 dx \\ \text{ but recall } x^2=u \\ \text{ so we have } \frac{1}{2}u du=x^3 dx$ that third line said I multiplied both sides by 1/2x^2

14. amyna

oh okay! thats more clear! Thanks!

15. freckles

it was just a copy and paste of what I said earlier :p $\frac{1}{2}x^2 \cdot 2x dx =\frac{2}{2} x^3 dx=x^3 dx$

16. anonymous

where is this $$\dfrac{1}2x^2$$ coming from...

17. freckles

we have to write x^3 dx in terms of u

18. freckles

that is where it comes from

19. anonymous

Oh nevermind, it's to eliminate the 2 and to obtain x$$^3$$ on the right side. Nvm.

20. jacobciezki

Why are you girls still in her