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neverforgetvivisteeBest ResponseYou've already chosen the best response.0
give me edals
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
oh that was annoying i cldnt type
 2 years ago

neverforgetvivisteeBest ResponseYou've already chosen the best response.0
give me medals free medals for everyone
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
can you write the equation again please :D
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
\[ \frac{d \ }{dx} \int_{17}^x \sin(t^2)/t \ dt \]
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
d/dx(sinx^2/x)  d/dx(sin(17)/17)
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
look at the earlier example with ln
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
wasn't it d/dx(F(x)F(17))
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
oh i see where i went wrong!!!!
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
Yes, but F is not the integrand.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
K just tell me the answer
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
Look at the ln example again.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
In the example we subsituted t for x
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
In the example we subsituted t for x
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
\[ \frac{d \ }{dx} \int_2^x \ln(t^2+1) \ dt \]
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
What is the value of that expression?
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
i dont know i am feeling very stupid!!!!!! dF/dx=ln(x^2+1)
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
If \[ F(t) = \int \ln(t^2+1) \ dt \] then \[ \int_2^x \ln(t^2+1) \ dt = F(x)  F(2) \]. Hence \[\frac{d \ }{dx} \int_2^x \ln(t^2+1) \ dt = \frac{d \ }{dx} (F(x)  F(2)) \]
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
and by the Fund Theorem of Calculus, dF/dx = ln(x^2 + 1). Also (d/dx)F(2) = 0 because F(2) is a number, a constant. Hence the entire expression is just ln(x^2+1)
 2 years ago

missyfredtomBest ResponseYou've already chosen the best response.0
James do you think you help me please?
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
So, return now to the next example where the integrand has a sin function. What is the value of that derivative?
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
@mft, I'll try and get to it. unfortunately you're not the first to ask.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
dont take james away form me:(
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
quick rld613. I want to move on with you to yet another example afterwards
 2 years ago

HeroBest ResponseYou've already chosen the best response.0
rld said she didn't need OS anymore
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
so (d/dx) int_17^x sin(t^2)/t dt = ...
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
i didnt get that why is 17 to th epower of x
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
\[ (d/dx) \int_{17}^x \sin(t^2)/t \ dt \]
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
evaluate. What is the that equal to.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
y is it wrong what i showed u b4?
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
plz be nice to me and show me all the step? :D
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
No. You write out the steps, following line by the line the example we just used for ln. I'm going to help someone else for a while and expect the right answer when I get back ;)
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
I'm serious. And I'll be back in 5 minutes, so hurry.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
u did u come back already!!!
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
K can u walk me thru the steps cuz like i bever learnt this stuff? YOu r so scary LOL
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
I was hoping i wld have the answer b4 u wld return
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
Exactly as before, exactly, let \[ F(t) = \int \sin(t^2)/t \ dt \] Then \[ \int_{17}^x \sin(t^2)/t \ dt = F(x)  F(17) \] Thus the derivative of this definite integral \[ \frac{d\ }{dx} (F(x)  F(17)) = ... \]
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
That is where i am going wrong
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
like we've seen, we actually don't need an explicit formula for F(x). We just need to know it is this integral and then use the Fundamental Theorem of Calculus.
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
What is dF/dx here? What is it equal to?
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
By the FTC, dF/dx = .... what?
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
You are forsure ready to kill me!!!!!!!!!!!!!!!
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
You are forsure ready to kill me!!!!!!!!!!!!!!!
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
correct. Hence the derivative wrt (with respect to) x of the entire integral equals what?
 2 years ago

pokemon23Best ResponseYou've already chosen the best response.1
hey james can you help me with math?
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
This thing ... what's it equal to?
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
sinx^2/x????? this is a guess
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
it shouldn't be guess. it is exactly right.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
That is what i thought in the first place but i left out by accident the squared
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
I can be so annoying sometimes
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
Now one more to make sure you really understand. Evaluate this: \[ \frac{d \ }{dx} \int_x^{x^2} \sqrt{t^3+1} \ dt \]
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
Now write out the steps. This problem isn't exactly the same as the others.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
\[d/dx=(\sqrt{x ^{6}+1}\sqrt{x ^{3}+1})\]
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
I think it was suppossed to be dF/dx
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
The expression is equal to \[ \frac{d \ }{dx} \left( F(x^2)  F(x) \right) \ \ \ \ \ \ (*)\] where by the Fund Theorem of Calculus, \[ dF/dx = \sqrt{x^3+1} \] Now given that, evaluate the first expression, (*).
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
hint: you need to use the chain rule.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
james u gotta help me out on this one
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
you think about it for a bit and write the answer sometime in the next day when you know what's going on.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
I will call you back when i get the
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
\[2x \sqrt{x ^{6}+1}  \sqrt{x ^{3}+1}\] Here is my answer. Thanks james for your help. I really appreciate it
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
One more variation they might throw at you in the exam. Evaluate: \[ \frac{d^2 \ }{dx^2} \int_2^x \ln(\cos t) \ dt \]
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
Oh this is very simple there is just one small catch that you have to differentiate it twice
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
d/dx(ln(cosx)) (1/cosx)*sin(x)= sin(x)/cos(x) tan(x)
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
I think that is the answer. I took my final exam already and it was basically simple except ofr a related rates problem. Going on vacation for a month So see u then. Thanks for your help james
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
Thanks for helping me out
 2 years ago

JamesJBest ResponseYou've already chosen the best response.4
sure. have a good vacation.
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
U better take a vacation from OS tooo!!! :D
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
Ya u need a break to refresh again
 2 years ago

rld613Best ResponseYou've already chosen the best response.0
OS wldnt survive without James myinaya satellite and Hero
 2 years ago
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