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QRAwarrior

  • 3 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.

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  1. Mimi_x3
    • 3 years ago
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    Then where do you needhelp with?

  2. QRAwarrior
    • 3 years ago
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    Evaluating

  3. QRAwarrior
    • 3 years ago
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    Where do you people get your bike avatars from?

  4. QRAwarrior
    • 3 years ago
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    I do not want "Google" as an answer... :O

  5. lgbasallote
    • 3 years ago
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    looks trig sub...have you learned that yet?

  6. QRAwarrior
    • 3 years ago
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    Yes

  7. lgbasallote
    • 3 years ago
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    but we really did gust google this! i swear! :(

  8. Mimi_x3
    • 3 years ago
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    What's the whole question?

  9. lgbasallote
    • 3 years ago
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    just*

  10. lgbasallote
    • 3 years ago
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    |dw:1337521244254:dw|

  11. QRAwarrior
    • 3 years ago
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    |dw:1337521266266:dw|

  12. QRAwarrior
    • 3 years ago
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    Yes I know that trig sub.

  13. lgbasallote
    • 3 years ago
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    |dw:1337521291094:dw|

  14. QRAwarrior
    • 3 years ago
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    But ultimately, you have to put a -4 into a trigonometric function's argument. How will that work?

  15. Mimi_x3
    • 3 years ago
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    the problem is subbing in the limits???

  16. LagrangeSon678
    • 3 years ago
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    convert the limits when using the trig sub

  17. lgbasallote
    • 3 years ago
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    dont forget to change back to x before evaluating

  18. Mimi_x3
    • 3 years ago
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    No, you don't need to convert back

  19. lgbasallote
    • 3 years ago
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    otherwise you'll have to convert the limits in terms of theta

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

  21. lgbasallote
    • 3 years ago
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    yep.. \[\int \sec^3 \theta d\theta\]

  22. QRAwarrior
    • 3 years ago
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    Then what is limits of integration wrt θ?

  23. QRAwarrior
    • 3 years ago
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    What is arctan(-4)?

  24. QRAwarrior
    • 3 years ago
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    How did you get that?

  25. QRAwarrior
    • 3 years ago
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    I got sec^3(θ)

  26. lgbasallote
    • 3 years ago
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    it was sec^3 theta...ohh woops

  27. lgbasallote
    • 3 years ago
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    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. QRAwarrior
    • 3 years ago
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    |dw:1337523905957:dw| @LagrangeSon678 @shivam_bhalla

  29. QRAwarrior
    • 3 years ago
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    @experimentX

  30. experimentX
    • 3 years ago
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    evaluate it individually .. \[ \int \sec \theta d\theta = \ln |\sec\theta + \tan\theta|\]

  31. experimentX
    • 3 years ago
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    this is a lot better http://answers.yahoo.com/question/index?qid=20110524035942AAXxTdM

  32. shivam_bhalla
    • 3 years ago
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    @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. shivam_bhalla
    • 3 years ago
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    You can go ahead and derive this

  34. shivam_bhalla
    • 3 years ago
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    I forgot the dx in the question :P

  35. QRAwarrior
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    brb

  38. shivam_bhalla
    • 3 years ago
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    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. QRAwarrior
    • 3 years ago
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    @shivam_bhalla look at my recent post above

  40. QRAwarrior
    • 3 years ago
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    Those are two functions!

  41. QRAwarrior
    • 3 years ago
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    I just realized! I would have to use the washer.

  42. shivam_bhalla
    • 3 years ago
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    @QRAwarrior , I am not so good at this. @TuringTest can surely help you in this :)

  43. QRAwarrior
    • 3 years ago
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    Alright thanks your help for the above.

  44. QRAwarrior
    • 3 years ago
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    @TuringTest help please @amistre64 @Hero @asnaseer

  45. QRAwarrior
    • 3 years ago
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    @FoolForMath would you mind helping me here?

  46. QRAwarrior
    • 3 years ago
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    Someone is bound to come!

  47. QRAwarrior
    • 3 years ago
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    @apoorvk help please?

  48. QRAwarrior
    • 3 years ago
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    Please look at the most recent question (it is the one with the sketch just above, NOT THE OPENING POST)

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

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