## anonymous 4 years ago Evaluate the definite integral from u = 0 to u = -4 of: \sqrt{1 + u^2} dx As you may have noticed, I have already done U-sub.

1. Mimi_x3

Then where do you needhelp with?

2. anonymous

Evaluating

3. anonymous

Where do you people get your bike avatars from?

4. anonymous

5. anonymous

looks trig sub...have you learned that yet?

6. anonymous

Yes

7. anonymous

but we really did gust google this! i swear! :(

8. Mimi_x3

What's the whole question?

9. anonymous

just*

10. anonymous

|dw:1337521244254:dw|

11. anonymous

|dw:1337521266266:dw|

12. anonymous

Yes I know that trig sub.

13. anonymous

|dw:1337521291094:dw|

14. anonymous

But ultimately, you have to put a -4 into a trigonometric function's argument. How will that work?

15. Mimi_x3

the problem is subbing in the limits???

16. anonymous

convert the limits when using the trig sub

17. anonymous

dont forget to change back to x before evaluating

18. Mimi_x3

No, you don't need to convert back

19. anonymous

otherwise you'll have to convert the limits in terms of theta

20. anonymous

Ok let me see what happens: - tan(θ) = u/1 - sec(θ) = \sqrt{1 + u^2} Then, sec^2(θ)dθ = du

21. anonymous

yep.. $\int \sec^3 \theta d\theta$

22. anonymous

Then what is limits of integration wrt θ?

23. anonymous

What is arctan(-4)?

24. anonymous

How did you get that?

25. anonymous

I got sec^3(θ)

26. anonymous

it was sec^3 theta...ohh woops

27. anonymous

sec^3 theta = (sec^2 theta)sec theta (1+ tan^2 theta) sec theta $\int \sec \theta + \tan^2 \theta \sec \theta$ lol got me stuck now

28. anonymous

|dw:1337523905957:dw| @LagrangeSon678 @shivam_bhalla

29. anonymous

@experimentX

30. experimentX

evaluate it individually .. $\int \sec \theta d\theta = \ln |\sec\theta + \tan\theta|$

31. experimentX

this is a lot better http://answers.yahoo.com/question/index?qid=20110524035942AAXxTdM

32. anonymous

@QRAwarrior , i just remember this $\int\limits_{}^{}\sqrt{x^2+a^2} = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log{|x+\sqrt{x^2+a^2}|}+C$

33. anonymous

You can go ahead and derive this

34. anonymous

I forgot the dx in the question :P

35. anonymous

Ok, skrew that question and instead would you mind looking at this: You have the curves x = (y-7)^2, and x = 4 that enclose a region. You must rotate this region about y = 5. |dw:1337525316103:dw| I need to use the shell method here, but it looks like as if I will get two cylinders here. Thanks for the help on the opening post question...

36. experimentX

I think that's formula for standard integral ... what do we call it ... i have bunch of them in my books ... but they are derived in the same way!!

37. experimentX

brb

38. anonymous

slight Correction: $\int\limits\limits_{}^{}\sqrt{x^2+a^2} \space \space dx = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log{|x+\sqrt{x^2+a^2}|}+C$

39. anonymous

@shivam_bhalla look at my recent post above

40. anonymous

Those are two functions!

41. anonymous

I just realized! I would have to use the washer.

42. anonymous

@QRAwarrior , I am not so good at this. @TuringTest can surely help you in this :)

43. anonymous

Alright thanks your help for the above.

44. anonymous

@TuringTest help please @amistre64 @Hero @asnaseer

45. anonymous

@FoolForMath would you mind helping me here?

46. anonymous

Someone is bound to come!

47. anonymous

48. anonymous

Please look at the most recent question (it is the one with the sketch just above, NOT THE OPENING POST)

49. experimentX

http://www.wolframalpha.com/input/?i=x+%3D+%28y-7%29^2%2C++x%3D4 $\int_{5}^{9}2\pi (y-7)(y-7)^2 dy$