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: Evaluating Definite Integral

  1. Jan 26, 2005 #1
    If I want to evaluate: [tex] \int^1_0 \frac {dx}{(x+1)^2} [/tex] I need to use the Fundamental Theorem of Calculus right? SO wouldn't I have to solve [tex] \int^b_a
    \frac{dx}{(x+1)^2} = \frac{(x+1)^3}{3} = \frac {8}{3} - \frac {1}{3} [/tex]? But the answer is [tex] \frac {1}{2} [/tex]
     
    Last edited: Jan 26, 2005
  2. jcsd
  3. Jan 26, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    There are a lot of errors there.How about making a substitution ??

    Daniel.

    P.S.You evaluated wrongly another integral,not the one u were supposed to...
     
  4. Jan 26, 2005 #3
    you're gona integrate that function.
    between the limits 1 and 0
    1/(x+1)^2 is the same as (x+1)^-2 {to the power neg two}
    when you integrate you add 1 to the power

    (x+1)^(-2+1) {to the power neg one}
    and then divide by this new value of the power
    (x+1)^-1
    -1
    rearanging the equation gives -1/(x+1)
    when you sub 1 for x you get -1/2
    when you sub 0 for x you get 1
    -1/2 + 1 you get 1/2
     
  5. Jan 26, 2005 #4
    I got it. It's [tex] \int^1_0 \frac {dx}{(x+1)^2} = \frac {-1}{x+1} [/tex]
    So [tex] F(1) - F(0) = \frac {1}{2} [/tex]
     
  6. Jan 26, 2005 #5

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Not really...What about the integration limits?

    As for the limit part,could u rewrite it in an intelligible form...?

    Daniel.
     
  7. Jan 26, 2005 #6
    I am not sure what you mean. I was just using the fact that [tex] \int^b_a f(u) \ du = F(b) - F(a) [/tex]. Why wouldn't my answer be correct?

    Thanks
     
  8. Jan 26, 2005 #7

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Because it shouldn't depend on "x"...It should be a real number...Not a function...

    Daniel.
     
  9. Jan 26, 2005 #8

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Where did the rest of the limit go??

    Daniel.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook