Here's the question you clicked on:
swin2013
Integral question?
\[\int\limits \sin \theta (\cos \theta +5)^7 d \theta\]
My work: u = \[\cos \theta + 5\] \[du / d \theta\] : \[\sin \theta\] du = \[\sin \theta d \theta \] \[\theta = \pi \] \[\theta = 0 \] u = 4 u = 6 \[\int\limits\limits (from 4 - 6) u^7 du \]
Hmm I think you're going from 6 to 4 actually aren't you?
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
lol yea, i stated the lower boundary first
so is it [-cos (theta + 5) ^8/8 ] from 4-6?
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.
\[\large \frac{1}{8}u^8|_{u=4}^6\]
lol yea, the answer is 207, 760 but i don't get that :(
See how you changed the limits to `u=`? Those are values you'll be plugging into `u`. Simple as that.
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.
i know, I changed the theta values to u values
oh... i thought that you replace u with u= costheta +5..
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.
Confused about that part? <:o
holy cow... i looked back at my notes. that is correct lol!
lollll thanks!! and i also have another question. but i'll post it on a different one lol