anonymous
  • anonymous
How do I integrate this equation? http://imgur.com/f7gCS
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amistre64
  • amistre64
would you just integrate both sides and then figure out the carnage? something akin to expanding is my first thought
amistre64
  • amistre64
the right side might become hat/Mcp ... but i got no idea what those letters are spose to represent
apoorvk
  • apoorvk
1/(T-Tw) can be written as (T-Tw)^(-1)... now i believe Tw is a constant.. so integral of any (ax+b)^n with respect to x is [(ax+b)^(n+1)]/[a(n+1)] plus constant.. which wont be present as the integration is definite..

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
I have the solution, however I just don't know the steps in between. I am a bit rusty on my integration. Here's the solution if it helps.
1 Attachment
amistre64
  • amistre64
lol, well I got the right side :) except for a - prolly
anonymous
  • anonymous
Sorry Tw is just temperature of water T0 is initial temperature
amistre64
  • amistre64
\[\int_{0}^{t}dt\to t-0=t\]
amistre64
  • amistre64
i cant make out what the left side is spose to "be" in order to even try to get it to look like the answer
anonymous
  • anonymous
Me neither, it's driving me insane. I think it's just confusing purely because there's notation rather than numbers.
amistre64
  • amistre64
yeah, its like it was pulled out of thin air and we are spose to simply "know" what it is :)
amistre64
  • amistre64
is Tw constant? and T variable?
amistre64
  • amistre64
or both variable and subnotated from some evil purpose?
amistre64
  • amistre64
u = t-tw du = 1 -(t'w+tw') ??? i cant even make out what to u sub even if we could u sub
anonymous
  • anonymous
Yes Tw is constant
amistre64
  • amistre64
then maybe: u = (T-K) du = 1 dT du = dT du/u int up to ln(T-K). ln(T-K) - ln(To-K) = ln((T-Tw)/(To-Tw))
amistre64
  • amistre64
looks almost doable
amistre64
  • amistre64
-2 1-3 -1(3-1) 2 --- = --- = ------ = -- -4 1-5 -1(5-1) 4 i spose that good
amistre64
  • amistre64
\[\int_{T_o}^{T}\frac{dT}{T-T_w}=-\frac{ha}{Mc_p}\int_{0}^{t}dt\] \[\Large\left.ln(T-T_w)\right|^{T}_{T_o}=-\frac{ha}{Mc_p}t|^{t}_{0}\] \[\Large ln(T-T_w)-ln(T_o-T_w)=-\frac{ha}{Mc_p}(t-0)\] and then it plays out from there
anonymous
  • anonymous
Would it not be at the 3rd step \[\ln (T-T _{w})-\ln(T _{0}-T)\] because we have to sub in the limits?
amistre64
  • amistre64
You sub into "T" ... Tw is a constant; so think of it like say "4"
amistre64
  • amistre64
assume the limits to be numbers like 3 and 5 ln(T-"4") from 3 to 5 is just: ln(5-"4") - ln(3-"4") for example
anonymous
  • anonymous
lol, I am idiot, makes perfect sense. Seriously need to brush up on integration!!! Thank you for the help, I was putting out my hair for a long time!
amistre64
  • amistre64
:) yw, and good luck

Looking for something else?

Not the answer you are looking for? Search for more explanations.