## Luigi0210 11 months ago Integration:

1. Luigi0210

$\LARGE \int_{-1}^{0}~\frac{e^{1/x}}{x^3}~dx$

2. ganeshie8

sub u = 1/x

3. myininaya

try letting u=1/x so x=1/u

4. dan815

then do parts

5. Joshyboi25tolyfe

Guys guys... In the eyes of god, mathematics doesn't exist! Now, let's all hold hands and pray.

6. ganeshie8

yeah u can't avoid parts i think

7. dan815

mathematics is a language and God gave us languages

8. dan815

9. Joshyboi25tolyfe

LOLOL ^

10. dan815

:)

11. Luigi0210

$\LARGE \int_{-1}^{0}~\frac{e^{1/x}}{x^3}~dx$ $\LARGE =\int_{-1}^{0}~\frac{1}{x}~e^{1/x}~\frac{1}{x^2}~dx$ $$\Large u=1/x$$ and $$\Large du=-\frac{1}{x^2}dx$$ $\LARGE \int_{-1}^{0}~ue^udu$ And then use parts like dan said?

12. Luigi0210

*$\LARGE -\int_{-1}^{0}~ue^udu$

13. myininaya

you should have an improper integral

14. Luigi0210

$\LARGE \LARGE \lim_{t \rightarrow 0} \int_{-1}^{t}~ue^udu~$?

15. myininaya

of x is between -1 and 0 and u=1/x |dw:1402252341171:dw|

16. myininaya

as we approach 0 from the left what is u getting approaching?

17. myininaya

|dw:1402252495152:dw|

18. myininaya

we are looking to the left of 0 because our interval is -1 to 0 none of our values occur to the right of 0 so we won't bother to look there

19. myininaya

i'm asking him to evaluate the following: $\lim_{x \rightarrow 0^-}\frac{1}{x}$

20. myininaya

lugi0210 just read the graph above as our x values get near the 0 number (from the left) what do your u values (or if you want call them y values) do?

21. Luigi0210

$$\Large -\infty$$?

22. myininaya

right so i'm going to change one thing in your lim from earlier $\LARGE \LARGE \lim_{t \rightarrow - \infty} \int\limits_{-1}^{t}~ue^udu~$

23. myininaya

i think there should be a negative in front of that

24. myininaya

$- \LARGE \LARGE \lim_{t \rightarrow - \infty} \int\limits\limits_{-1}^{t}~ue^udu~$

25. myininaya

you know from the du=-1/x^2 dx thing

26. myininaya

now use integration by parts then evaluate the limit

27. Luigi0210

Alright, I see it now, it was the limits that was throwing me off >_< Thank you myininaya :)

28. ganeshie8

if u feel lazy about changing the bounds, you may try below : 1) Find the indefinite integral first 2) plugin the bounds

29. myininaya

@Luigi0210 did you get it?