A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
solving for g'(x) when g(x)=integral from sqrt(x) to x^2, (sin t)(sqrt t) dt
anonymous
 3 years ago
solving for g'(x) when g(x)=integral from sqrt(x) to x^2, (sin t)(sqrt t) dt

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0derivative of the integral is the integrand, plus chain rule replace \(t\) by \(x^2\) and multiply by the derivative of \(x^2\) get \[\sin(x^2)\sqrt{x^2}\times 2x\] for the top part bottom part is the same, but make it negative

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I think I am suppose to break it up. integral from sqrt x to 0 plus 0 to x^2. But i have no idea why this is the way to do it

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes but you can break up anyway you like

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the top part gives what i wrote above, the bottom part is analogous, just make it negative

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the bottom can be any number??

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I know I'm suppose to use the second fundamental theorem

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes \[\int_{\sqrt{x}}^{x^2}f(t)dt=\int_{\sqrt{x}}^af(t)dt+\int_a^{x^2}f(t)dt\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0My teacher chose 0 though. Is there a reason for that? should I just choose 0 everytime?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0take the derivative of the second part, get \(f(x^2)\times 2x\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the derivative of the first part is \(f(\sqrt{x})\times \frac{1}{2\sqrt{x}}\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0if you like to pick zero, go ahead a pick zero makes no difference

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Ok I understand it now. Thanks!!!! :)
Ask your own question
Sign UpFind more explanations on OpenStudy
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.