1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculus problem: Integral of sqrt(1/4-(x+3)^2

  1. Sep 17, 2013 #1
    I've been trying to solve this integral for a very long time!
    Problem: Integral of sqrt(1/4-(x+3)^2

    Effort: I have tried multiplying by sqrt(1/4) to get rid of the 4 so it can become a 1, so it will match up with inverse sine's derivative. After that I got kind of lost, since I don't know what happens or what will (x+3)^2, will become. I know what the answer should be like, but I want to do it without using that special formula, that they provide.

    I know there's some trick because I didn't in high school, however, I don't recall it. I don't want to use that simple formula because it doesn't really tell you what's happening in the integration process. Can someone help me out? Thanks!
     
    Last edited: Sep 17, 2013
  2. jcsd
  3. Sep 17, 2013 #2

    rock.freak667

    User Avatar
    Homework Helper

    [tex] \int \sqrt{\frac{1}{4-(x+3)^2}}dx [/tex]

    If that is your integral, you could simplify this to

    [tex] \int \frac{1}{\sqrt{4-(x+3)^2}}dx[/tex]

    Then try a trig substitution.

    Think of sin2A+cos2A=1
     
  4. Sep 17, 2013 #3
    Yeah that is, I know it's suppose to be inverse sine and then I try getting rid of the 4 by multiplying sqrt(1/4) and then I get lost. Extra hints would help, thanks!
     
  5. Sep 17, 2013 #4

    rock.freak667

    User Avatar
    Homework Helper

    Can you show your steps? It might be hard to give you a hint when I don't really know where you get lost.
     
  6. Sep 17, 2013 #5
    I've attached a file, of what I have done so far. The "question mark" is where I'm stuck. And am I doing this step, right? Thanks!
     

    Attached Files:

  7. Sep 17, 2013 #6

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It might help to do the substitution u = (x+3)/2
     
  8. Sep 17, 2013 #7
    i figured it out! i used u-substitution to make the integral simpler and then i factored out the 4.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Calculus problem: Integral of sqrt(1/4-(x+3)^2
Loading...