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!

Early Calc2 HW Help

  1. Oct 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Solve the Integral
    [tex]\int (2 + 2x - x^2)^{3/2} dx[/tex]

    2. The attempt at a solution
    I have looked at integration tables, u-substitution, and integration by parts but none of the above seem to be working.

    U-Substitution wouldn't work because the du would be inside the integrand.
    I tried parts with U=[tex](2 + 2x - x^2)^{3/2}[/tex] and DV=dx , but that result brought me back to the original integral.

    What should I be using here that I am missing?
  2. jcsd
  3. Oct 25, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    What if you separated out 2 + 2x - x^2 and sqrt(2 + 2x - x^2), then tried integ. by parts?
  4. Oct 25, 2007 #3


    User Avatar
    Homework Helper

    Have you had trigonometric substitutions yet? (Square roots or fractional exponents with 2 in the denominator are usually a sign that you'll want them.)

    If you have, you'll need to do a couple of layers of substitution. You'd start by completing the square under the radical. You'll get a difference of two squares raised to the 3/2 power, or 1/2 power cubed. You'd then do a u-substitution, then the appropriate trig substitution. (It ain't gonna be pretty, but integrating fractional powers of quadratic polynomials generally aren't...)

    I should comment that integration by parts should only be considered if the "v du" integral you're going to get is something you actually know how to integrate (and preferably should be easier than the integral you began with -- or at worst, equally difficult, but related)...
    Last edited: Oct 25, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Early Calc2 HW Help
  1. Linear Algebra hw help (Replies: 3)

  2. HW help (Replies: 4)

  3. Hw help (Replies: 4)

  4. Calculus 3 hw help (Replies: 2)