Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

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

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
so the answer is?
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
oh that was annoying i cldnt type
 2 years ago

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
can you write the equation again please :D
 2 years ago

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
d/dx(sinx^2/x)  d/dx(sin(17)/17)
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
where did i go wrong?
 2 years ago

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
wasn't it d/dx(F(x)F(17))
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
oh i see where i went wrong!!!!
 2 years ago

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
F(x)=cosx/x???
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
K just tell me the answer
 2 years ago

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
In the example we subsituted t for x
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
In the example we subsituted t for x
 2 years ago

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

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

rld613 Group TitleBest 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

JamesJ Group TitleBest 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

JamesJ Group TitleBest 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

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

JamesJ Group TitleBest 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

JamesJ Group TitleBest 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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
dont take james away form me:(
 2 years ago

missyfredtom Group TitleBest ResponseYou've already chosen the best response.0
i can wait
 2 years ago

JamesJ Group TitleBest 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

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

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
i didnt get that why is 17 to th epower of x
 2 years ago

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

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
y is it wrong what i showed u b4?
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
plz be nice to me and show me all the step? :D
 2 years ago

JamesJ Group TitleBest 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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
LOL see u later :D
 2 years ago

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
u did u come back already!!!
 2 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
What's the answer?
 2 years ago

rld613 Group TitleBest 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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
I was hoping i wld have the answer b4 u wld return
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
teh answer wld sinx/x?
 2 years ago

JamesJ Group TitleBest 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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
iSo what is F(x)?????
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
That is where i am going wrong
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
oh i know si(x)?
 2 years ago

JamesJ Group TitleBest 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

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

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
You are forsure ready to kill me!!!!!!!!!!!!!!!
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
You are forsure ready to kill me!!!!!!!!!!!!!!!
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
dF/dx= sinx^2/x
 2 years ago

JamesJ Group TitleBest 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

pokemon23 Group TitleBest ResponseYou've already chosen the best response.1
hey james can you help me with math?
 2 years ago

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
sinx^2/x????? this is a guess
 2 years ago

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
oh ya !!!!!!!!
 2 years ago

rld613 Group TitleBest 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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
I can be so annoying sometimes
 2 years ago

JamesJ Group TitleBest 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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
oh u r so funny!!!
 2 years ago

JamesJ Group TitleBest 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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
ok give me a sec
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
\[d/dx=(\sqrt{x ^{6}+1}\sqrt{x ^{3}+1})\]
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
This one i guessed
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
I think it was suppossed to be dF/dx
 2 years ago

JamesJ Group TitleBest 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

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
ok so let me try that
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
james u gotta help me out on this one
 2 years ago

JamesJ Group TitleBest 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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
alrighty thanks james
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
I will call you back when i get the
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
I got the answer :D
 2 years ago

rld613 Group TitleBest 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

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
that's it. Good
 2 years ago

JamesJ Group TitleBest 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

rld613 Group TitleBest 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

rld613 Group TitleBest 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

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
exactly, good.
 2 years ago

rld613 Group TitleBest 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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
oh u are here LOL
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
Thanks for helping me out
 2 years ago

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

rld613 Group TitleBest ResponseYou've already chosen the best response.0
U better take a vacation from OS tooo!!! :D
 2 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.4
I might just do that.
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
Ya u need a break to refresh again
 2 years ago

rld613 Group TitleBest ResponseYou've already chosen the best response.0
OS wldnt survive without James myinaya satellite and Hero
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.