## Luigi0210 Group Title Integration: 2 months ago 2 months ago

1. Luigi0210 Group Title

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

2. ganeshie8 Group Title

sub u = 1/x

3. myininaya Group Title

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

4. dan815 Group Title

then do parts

5. Joshyboi25tolyfe Group Title

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

6. ganeshie8 Group Title

yeah u can't avoid parts i think

7. dan815 Group Title

mathematics is a language and God gave us languages

8. dan815 Group Title

9. Joshyboi25tolyfe Group Title

LOLOL ^

10. dan815 Group Title

:)

11. Luigi0210 Group Title

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

12. Luigi0210 Group Title

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

13. myininaya Group Title

you should have an improper integral

14. Luigi0210 Group Title

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

15. myininaya Group Title

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

16. myininaya Group Title

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

17. myininaya Group Title

|dw:1402252495152:dw|

18. myininaya Group Title

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 Group Title

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

20. myininaya Group Title

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 Group Title

$$\Large -\infty$$?

22. myininaya Group Title

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 Group Title

i think there should be a negative in front of that

24. myininaya Group Title

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

25. myininaya Group Title

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

26. myininaya Group Title

now use integration by parts then evaluate the limit

27. Luigi0210 Group Title

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

28. ganeshie8 Group Title

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

29. myininaya Group Title

@Luigi0210 did you get it?