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swin2013
 2 years ago
Integral question?
swin2013
 2 years ago
Integral question?

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swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits \sin \theta (\cos \theta +5)^7 d \theta\]

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0My work: u = \[\cos \theta + 5\] \[du / d \theta\] : \[\sin \theta\] du = \[\sin \theta d \theta \] \[\theta = \pi \] \[\theta = 0 \] u = 4 u = 6 \[\int\limits\limits (from 4  6) u^7 du \]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Hmm I think you're going from 6 to 4 actually aren't you?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Oh 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

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0lol yea, i stated the lower boundary first

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0so is it [cos (theta + 5) ^8/8 ] from 46?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1No, 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
 2 years ago
Best ResponseYou've already chosen the best response.1\[\large \frac{1}{8}u^8_{u=4}^6\]

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0lol yea, the answer is 207, 760 but i don't get that :(

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1See how you changed the limits to `u=`? Those are values you'll be plugging into `u`. Simple as that.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1It should be 201,760. Typo maybe? :o I'll check it on Wolfram real quick to make sure I didn't make a mistake.

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0i know, I changed the theta values to u values

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0oh... i thought that you replace u with u= costheta +5..

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1If 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
 2 years ago
Best ResponseYou've already chosen the best response.1Confused about that part? <:o

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0holy cow... i looked back at my notes. that is correct lol!

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0lollll thanks!! and i also have another question. but i'll post it on a different one lol
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