Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

Find \(\frac{df}{dx}\) where \[f(x) = \int_{-x}^{x^2}\frac{1}{\sqrt{1+t^6}}dt\] for x>0 How to start??

See more answers at
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.

Get this expert

answer on brainly


Get your free account and access expert answers to this and thousands of other questions

So this is one of those problems that involves requires you to apply the FTC Part 1. The Fundamental Theorem of Calculus part 1 is,\[\huge \frac{d}{dx}\int\limits_c^x f(t) dt=f(x)\] With this problem, we have an function of x within the upper and lower limits, so it'll look a bit different.\[\large \frac{d}{dx}\int\limits_{-x}^{x^2}f(t)dt=f(x^2)\color{blue}{(\frac{d}{dx}x^2)}-f(-x)\color{blue}{(\frac{d}{dx}-x)}\]The blue pieces are there because we have to apply the chain rule.
Fundamental Theorem of Integral Calculus will get you started. \(f(x) = \int\limits_{-x}^{x^{2}}g(t)\;dt\;=\;G(x^{2}) - G(-x)\) Where \(G(x)\) is an antiderivative of \(g(x)\). Chain Rule will get us the rest of the way. \(\dfrac{d}{dx}\left(G(x^{2}) - G(-x)\right)\;=\;g(x^{2})\cdot (2x) - g(-x)\cdot (-1)\)

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

I'm sorry... I was so blind... Thanks all!!!!
Don't forget that we DO have to believe that the antiderivative EXISTS! Good work.
f(-x) = f(x) too, I guess. Since it's an even function..

Not the answer you are looking for?

Search for more explanations.

Ask your own question