1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Rearranging of an equation

  1. Oct 9, 2013 #1
    i have a given equation of the following.

    W= -A1B1c[[itex]\frac{1}{-c+1}[/itex]B-c+1] where the part in brackets is the integrated function of B going from B1 to B2.

    then this equation somehow ends up like so


    (sorry for the messy format on the right hand side i couldn't get latex to work..)

    i don't know how they got from the first equation to the second equation. i don't know where to start because i don't know how certain terms were combined.
    Last edited: Oct 9, 2013
  2. jcsd
  3. Oct 9, 2013 #2


    Staff: Mentor

    Is this what you mean?

    $$W = -A_1B_1^c \int_{B_1}^{B_2} \frac{B^{-c + 1} dB}{-c + 1} $$
    If you right-click on the integral I wrote, you can see the LaTeX that creates it.
  4. Oct 9, 2013 #3
    thanks, however that wasn't what i meant. that function inside the bracket is 'already' integrated; what i was trying to say was that the limits just weren't taken.

    W = [itex]-A_1B_1^c \frac{B^{-c + 1}}{-c + 1}[/itex]
    Last edited by a moderator: Oct 9, 2013
  5. Oct 9, 2013 #4


    Staff: Mentor

    Are you sure that your antiderivative is correct? I'm thinking you might have made a mistake. What was the problem you started with?
  6. Oct 9, 2013 #5


    User Avatar
    Homework Helper

    So that's
    W = -A_1 B_1^c \frac{1}{-c+1}\left(B_2^{-c+1} - B_1^{-c + 1}\right)
    = \frac{A_1 B_1^c }{c-1}\left(B_2^{1-c} - B_1^{1-c}\right)
    after tidying up some signs.

    Now we pull a common factor of [itex]B_1^{1-c}[/itex] out of the bracket:
    W = \frac{A_1 B_1^c B_1^{1-c}}{c - 1} \left( \frac{B_2^{1-c}}{B_1^{1-c}} - 1\right)
    = \frac{A_1 B_1}{c - 1}\left( \left(\frac{B_2}{B_1}\right)^{1-c} - 1\right)

    Finally we flip the fraction in the bracket, remembering to multiply the exponent by -1 as we do so.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted