## anonymous one year ago Need Help! Evaluate the integral (1-x/x)^2 *dx

1. anonymous

|dw:1439271323768:dw|

2. ganeshie8

whats stopping you from expanding and working each term ?

3. anonymous

So I did it, but I got stuck on one part

4. anonymous

Let me draw it

5. anonymous

|dw:1439271526217:dw|

6. anonymous

What happens after this...because the solution manual is saying something else

7. ganeshie8

looks good! expand that out using the identity $(a-b)^2=a^2-2ab+b^2$

8. ganeshie8

|dw:1439271609165:dw|

9. ganeshie8

$\left(\frac{1}{x}-1\right)^2=?$

10. anonymous

OH thats what they did

11. anonymous

okay, I totally forgot about the identity and was wondering how they came up with the middle term

12. ganeshie8

it helps to review basic algebraic and trig identities while doing integrals

13. anonymous

I would honestly love doing integrals....but theres just so much algebra

14. ganeshie8

Exactly! calculus is always easy, its just the algebra part that is hard

15. ganeshie8

its not hard as such, its just pain

16. anonymous

lol tell me about it, I have my final in a few days..and im freaking out Either way, how is the middle term -2/x , im getting +2/x

17. ganeshie8

$(a-b)^2=a^2\color{red}{-}2ab+b^2$

18. anonymous

So it would be -2*(1/x)*(-1), right?

19. ganeshie8

$\left(\frac{1}{x}-1\right)^2=\frac{1}{x^2}-\frac{2}{x}+1$

20. anonymous

But the middle part is -2*(1/x)*(-1), so wouldnt that make it +2/x instead of -2/x?

21. ganeshie8

$\left(\frac{1}{x}-1\right)^2=(\frac{1}{x})^2-2(\frac{1}{x})(1)+1^2$

22. anonymous

why dont we multiply by negative, because isnt that the b value?

23. ganeshie8

$$a = \frac{1}{x}$$ $$b=1$$

24. anonymous

kk, I get it

25. ganeshie8

:)

26. ganeshie8

don't forget to integrate the terms

27. anonymous

btw are you in Uni?

28. anonymous

Also, how do we integrate 1/x^2?

29. Astrophysics

$\frac{ 1 }{ x^2 } = x^{-2} ~~~~~\int\limits \frac{ 1 }{ x^2 } dx = \int\limits x^{-2} dx = \frac{ x^{-1} }{ -1 }+C = - \frac{ 1 }{ x }+C$

30. anonymous

nvm, I watched this video https://www.youtube.com/watch?v=ZFZRid582Lk, and even though its in spanish...I figured it out, thanks though astro

31. ganeshie8

here is a trick question, $\int \frac{1}{x}~dx = ?$ @mary_am

32. anonymous

lnIxI + c

33. ganeshie8

nvm that video is a spoiler

34. Astrophysics

lol

35. anonymous

k im not dumb.. I knew what ∫1x dx was

36. anonymous

*THAT

37. ganeshie8

Ofcourse you're not, I see :)

38. Astrophysics

I am dumb, and yes I am xD

39. Astrophysics

40. Astrophysics

Eihsenag university

41. Astrophysics

We enjoy helping people, it's a good way to learn ourselves :-)

42. Astrophysics

They intertwine

43. Astrophysics

Thank you and you to!