Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Study23

Find the most general antiderivative of the following function (note I have NOT learned about integrals yet). I'm confused about the chain rule and the antiderivative. The function: 2x+5(1-x^2)^(-1/2)

  • one year ago
  • one year ago

  • This Question is Closed
  1. Argonx16
    Best Response
    You've already chosen the best response.
    Medals 1

    First of all, for the sake of simplicity, lets pretend that antiderivatives are the same as integrals (they pretty much are). Also, when I say\[\int\limits_{}{} \frac {2x+5}{\sqrt{1-x^2}}\] I mean "take the antiderivate of 2x+5(1-x^2)^(-1/2). So the first thing we notice is that we could rewrite the problem to \[\int\limits_ {}{} \frac {1}{\sqrt{1-x^2}} * 2x+5\] If we look on the left hand side, we notice that we have the term \[\int\limits_ {}{} \frac {1}{1-x^2}\] Which is the derivative of inverse sine \[\sin^{-1}\]

    • one year ago
  2. Argonx16
    Best Response
    You've already chosen the best response.
    Medals 1

    EDIT. I totally mean to have a square root sign under the 1-x^2 up there. My bad. So from that, we can conclude that inverse sine will have a part in this integral (antiderivative). So now that we know that inverse sine is part of the question, lets work through the integral again. \[\int\limits\limits\limits {}{} \frac{1}{\sqrt{1-x^2}} (2x+5)\] The 1-x^2 is the "driving function," or if you learn u-substitution later, the "U," meaning that if the "driving function/U" is responsible for the (2x+5) term per the chain rule. If this doesn't make any sense, just wait until you learn U-substitution (or read about it yourself!)

    • one year ago
    • Attachments:

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.