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ta123

  • 3 years ago

need help on the attachment @Calculus1

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  1. ta123
    • 3 years ago
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  2. ta123
    • 3 years ago
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    hey you know on the other problem you were helping me with lagrange?

  3. ta123
    • 3 years ago
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    what did you get for the answer because I got -4 and they counted it wrong

  4. LagrangeSon678
    • 3 years ago
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    i got 2

  5. LagrangeSon678
    • 3 years ago
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    are u sure you evaluated correctly

  6. ta123
    • 3 years ago
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    oh, made a stupid sign error

  7. ta123
    • 3 years ago
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    could you help me with this new problem on the attachment

  8. LagrangeSon678
    • 3 years ago
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    yeah let me look at it

  9. LagrangeSon678
    • 3 years ago
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    okay so this is what you wanna do, set u=x+4, then you have to then rewrite x in terms of u. You can do this simply by saying x=u-4

  10. ta123
    • 3 years ago
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    ok

  11. LagrangeSon678
    • 3 years ago
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    |dw:1321490017407:dw|

  12. LagrangeSon678
    • 3 years ago
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    |dw:1321490044699:dw|

  13. LagrangeSon678
    • 3 years ago
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    |dw:1321490067161:dw|

  14. ta123
    • 3 years ago
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    do you replug the original function into u after integrating

  15. LagrangeSon678
    • 3 years ago
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    yes after you, integrate, you must replace the orginal function

  16. ta123
    • 3 years ago
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    did you get u^2/2-3x*2U^(1/2) after integrating

  17. LagrangeSon678
    • 3 years ago
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    give me a sec

  18. LagrangeSon678
    • 3 years ago
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    i led you wrong, my mistake. What you want to do, is let u=sqrt(x+4), now we rewrite x interm of u. To do this simply:|dw:1321490856188:dw|

  19. LagrangeSon678
    • 3 years ago
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    okay, now you should get:|dw:1321490948435:dw|

  20. LagrangeSon678
    • 3 years ago
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    now let fix up that integral:|dw:1321491019469:dw|

  21. LagrangeSon678
    • 3 years ago
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    |dw:1321491091199:dw|

  22. LagrangeSon678
    • 3 years ago
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    now recall that u=sqrt(x+4), thus we can divide out the u in the denmominator and the sqrt(x+4) as so:|dw:1321491198348:dw| The two can be put outside the integral since it is a constant

  23. LagrangeSon678
    • 3 years ago
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    now simply we have:|dw:1321491263984:dw|

  24. LagrangeSon678
    • 3 years ago
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    next you have to integrate that, and then replace the u's. Then evaluate over your limits

  25. LagrangeSon678
    • 3 years ago
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    or, we could simply change the limits interms of u. Which would actaully be much eaier in this case. But i leave that up to you to decide on

  26. ta123
    • 3 years ago
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    sqrt(x+4) did both cancel out and when you replace the u on the bottom back to x+4 don't you have to do the same thing to the top?

  27. LagrangeSon678
    • 3 years ago
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    on top we had u^2-3, cause we replaced the x remeber

  28. ta123
    • 3 years ago
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    oh, ok also you forgot to label the endpoints on the integral

  29. LagrangeSon678
    • 3 years ago
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    well,i didnt forget, for me it is simpler to first leave the limits while i do the integration, since they really dont matter untill we get the antiderivative, which we then evlauate over the limits

  30. ta123
    • 3 years ago
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    I got -44

  31. ta123
    • 3 years ago
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    is that right?

  32. ta123
    • 3 years ago
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    ???

  33. LagrangeSon678
    • 3 years ago
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    yes i did,1 is the correct answer

  34. ta123
    • 3 years ago
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    Thanks could you help me with one more of these problem?

  35. LagrangeSon678
    • 3 years ago
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    sure

  36. LagrangeSon678
    • 3 years ago
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    did you post it already?

  37. ta123
    • 3 years ago
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    1 Attachment
  38. LagrangeSon678
    • 3 years ago
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    i cant open it

  39. ta123
    • 3 years ago
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  40. ta123
    • 3 years ago
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    could you open it?

  41. LagrangeSon678
    • 3 years ago
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    yeah, okay lets do this, can we multiply the x into the brackets, then seperate the integral into two spereate integrals:|dw:1321500013159:dw|

  42. LagrangeSon678
    • 3 years ago
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    now lets take out some constants: |dw:1321500075388:dw|

  43. LagrangeSon678
    • 3 years ago
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    now let try this, can we for the first integral, let x^2=u, then du=2xdx, which further means du/2x=dx

  44. LagrangeSon678
    • 3 years ago
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    now it should look something like this:|dw:1321500219046:dw|

  45. LagrangeSon678
    • 3 years ago
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    now we see that the x will divide out, and the 1/2 from the du can be taken outside the integral, so now we will get :|dw:1321500319063:dw|

  46. LagrangeSon678
    • 3 years ago
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    now 2*1/2 is simply 1, so we now have:|dw:1321500384165:dw|

  47. LagrangeSon678
    • 3 years ago
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    now we can integrate

  48. LagrangeSon678
    • 3 years ago
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    for the first integral, what i the antiderivative of f'? well its simply f, the orginal function , and the second integral is very simpyle to integrate

  49. LagrangeSon678
    • 3 years ago
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    |dw:1321500486597:dw|

  50. LagrangeSon678
    • 3 years ago
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    |dw:1321500522223:dw|

  51. LagrangeSon678
    • 3 years ago
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    but lets replace the u:|dw:1321500561883:dw|

  52. LagrangeSon678
    • 3 years ago
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    now you can evaluate this over you limits but remeber that you were given certain conditions, namely f(1)=3 and f(0)=1.so we have|dw:1321500688385:dw|

  53. LagrangeSon678
    • 3 years ago
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    furthermore:|dw:1321500784828:dw|

  54. LagrangeSon678
    • 3 years ago
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    Got it

  55. ta123
    • 3 years ago
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    yes, I was just was reviewing all the work, thanks!

  56. LagrangeSon678
    • 3 years ago
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    anytime:)soon you will be an expert on calculus and you will be helping others as well

  57. ta123
    • 3 years ago
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    I hope so, thanks again

  58. LagrangeSon678
    • 3 years ago
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    your welcome:)

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