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swin2013

  • 3 years ago

Integral question?

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  1. swin2013
    • 3 years ago
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    \[\int\limits \sin \theta (\cos \theta +5)^7 d \theta\]

  2. swin2013
    • 3 years ago
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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 \[\int\limits\limits (from 4 - 6) u^7 du \]

  3. swin2013
    • 3 years ago
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    @zepdrix

  4. zepdrix
    • 3 years ago
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    Hmm I think you're going from 6 to 4 actually aren't you?

  5. zepdrix
    • 3 years ago
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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

  6. swin2013
    • 3 years ago
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    lol yea, i stated the lower boundary first

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

  8. zepdrix
    • 3 years ago
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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.

  9. zepdrix
    • 3 years ago
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    \[\large \frac{1}{8}u^8|_{u=4}^6\]

  10. swin2013
    • 3 years ago
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    lol yea, the answer is 207, 760 but i don't get that :(

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

  12. zepdrix
    • 3 years ago
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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.

  13. swin2013
    • 3 years ago
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    i know, I changed the theta values to u values

  14. swin2013
    • 3 years ago
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    lol yea typo

  15. swin2013
    • 3 years ago
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    oh... i thought that you replace u with u= costheta +5..

  16. zepdrix
    • 3 years ago
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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.

  17. zepdrix
    • 3 years ago
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    Confused about that part? <:o

  18. swin2013
    • 3 years ago
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    holy cow... i looked back at my notes. that is correct lol!

  19. zepdrix
    • 3 years ago
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    dat swin :3

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

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