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swin2013 Group Title

Integral question?

  • one year ago
  • one year ago

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  1. swin2013 Group Title
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    \[\int\limits \sin \theta (\cos \theta +5)^7 d \theta\]

    • one year ago
  2. swin2013 Group Title
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    My work: u = \[\cos \theta + 5\] \[du / d \theta\] : \[\sin \theta\] du = \[\sin \theta d \theta \] \[\theta = \pi \] \[\theta = 0 \] u = 4 u = 6 \[\int\limits\limits (from 4 - 6) u^7 du \]

    • one year ago
  3. swin2013 Group Title
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    @zepdrix

    • one year ago
  4. zepdrix Group Title
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    Hmm I think you're going from 6 to 4 actually aren't you?

    • one year ago
  5. zepdrix Group Title
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    Oh it looks like you missed the negative when you took the derivative of your `u`. Maybe you just applied it to your integral, swapping the limits of integration? Or maybe you got lucky? XD lol

    • one year ago
  6. swin2013 Group Title
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    lol yea, i stated the lower boundary first

    • one year ago
  7. swin2013 Group Title
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    so is it [-cos (theta + 5) ^8/8 ] from 4-6?

    • one year ago
  8. zepdrix Group Title
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    No, if you're going to go through the trouble of changing the limits, then it means you're going to solve (all the way down to a numerical value) in `u`, no longer worrying about the function of `theta` you had before.

    • one year ago
  9. zepdrix Group Title
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    \[\large \frac{1}{8}u^8|_{u=4}^6\]

    • one year ago
  10. swin2013 Group Title
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    lol yea, the answer is 207, 760 but i don't get that :(

    • one year ago
  11. zepdrix Group Title
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    See how you changed the limits to `u=`? Those are values you'll be plugging into `u`. Simple as that.

    • one year ago
  12. zepdrix Group Title
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    It should be 201,760. Typo maybe? :o I'll check it on Wolfram real quick to make sure I didn't make a mistake.

    • one year ago
  13. swin2013 Group Title
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    i know, I changed the theta values to u values

    • one year ago
  14. swin2013 Group Title
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    lol yea typo

    • one year ago
  15. swin2013 Group Title
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    oh... i thought that you replace u with u= costheta +5..

    • one year ago
  16. zepdrix Group Title
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    If you `had not changed the limits of integration` then yes you would have had to do that before putting in the limits. But you changed your limits ~ No need to change back to costheta+5.

    • one year ago
  17. zepdrix Group Title
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    Confused about that part? <:o

    • one year ago
  18. swin2013 Group Title
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    holy cow... i looked back at my notes. that is correct lol!

    • one year ago
  19. zepdrix Group Title
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    dat swin :3

    • one year ago
  20. swin2013 Group Title
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    lollll thanks!! and i also have another question. but i'll post it on a different one lol

    • one year ago
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