anonymous
  • anonymous
Integral question?
Biology
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[\int\limits \sin \theta (\cos \theta +5)^7 d \theta\]
anonymous
  • anonymous
My work: u = \[\cos \theta + 5\] \[du / d \theta\] : \[\sin \theta\] du = \[\sin \theta d \theta \] \[\theta = \pi \] \[\theta = 0 \] u = 4 u = 6 \[\int\limits\limits (from 4 - 6) u^7 du \]
anonymous
  • anonymous
@zepdrix

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zepdrix
  • zepdrix
Hmm I think you're going from 6 to 4 actually aren't you?
zepdrix
  • zepdrix
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
anonymous
  • anonymous
lol yea, i stated the lower boundary first
anonymous
  • anonymous
so is it [-cos (theta + 5) ^8/8 ] from 4-6?
zepdrix
  • zepdrix
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.
zepdrix
  • zepdrix
\[\large \frac{1}{8}u^8|_{u=4}^6\]
anonymous
  • anonymous
lol yea, the answer is 207, 760 but i don't get that :(
zepdrix
  • zepdrix
See how you changed the limits to `u=`? Those are values you'll be plugging into `u`. Simple as that.
zepdrix
  • zepdrix
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.
anonymous
  • anonymous
i know, I changed the theta values to u values
anonymous
  • anonymous
lol yea typo
anonymous
  • anonymous
oh... i thought that you replace u with u= costheta +5..
zepdrix
  • zepdrix
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.
zepdrix
  • zepdrix
Confused about that part? <:o
anonymous
  • anonymous
holy cow... i looked back at my notes. that is correct lol!
zepdrix
  • zepdrix
dat swin :3
anonymous
  • anonymous
lollll thanks!! and i also have another question. but i'll post it on a different one lol

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