Results 1 to 3 of 3

Math Help - Partial fraction integration

  1. #1
    Member
    Joined
    Apr 2010
    Posts
    81

    Partial fraction integration

    <br />
\int\frac{6x^{2}-12x+27}{(x-4)(x^{2}+9)} <br />
= \frac{A}{x-4} + \frac{B x + C}{x^{2}+9}<br />

    Am I doing something wrong here?

    First, I simplify this
    <br />
3\int\frac{2x^{2}-4x+9}{(x-4)(x^{2}+9)}<br />

    \frac{A}{x-4}+\frac{BX+C}{x^2+9}<br />

    is this setup correct?

    <br />
A(x^2+9)+(BX+C)(x-4)=2x^{2}-4x+9<br />

    When I set x=4, I get an A value of 25/19

    This does not seem correct. My prof said we would ONLY get whole numbers for the example problems given.

    What should I do differently?

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    f(4) : A(4^2+9) = 32-16+9 \implies 25A = 25 \implies A=1
    Last edited by e^(i*pi); February 10th 2011 at 07:58 AM. Reason: latex
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Vamz View Post
    <br />
\int\frac{6x^{2}-12x+27}{(x-4)(x^{2}+9)} <br />
= \frac{A}{x-4} + \frac{B x + C}{x^{2}+9}<br />

    Am I doing something wrong here?

    First, I simplify this
    <br />
3\int\frac{2x^{2}-4x+9}{(x-4)(x^{2}+9)}<br />

    \frac{A}{x-4}+\frac{BX+C}{x^2+9}<br />

    is this setup correct?

    <br />
A(x^2+9)+(BX+C)(x-4)=2x^{2}-4x+9<br />

    When I set x=4, I get an A value of 25/19

    This does not seem correct. My prof said we would ONLY get whole numbers for the example problems given.

    What should I do differently?

    Thank you!
    Since you didn't show your work I can only guess that you have made an arithmetic error
    \displaystyle x=4 \implies A(4^2+9)+(Bx+c)(4-4)=2(4)^2-4(4)+9 \iff 25A=25 \implies A=1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another Partial Fraction Integration
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 11th 2011, 01:07 AM
  2. partial fraction - integration
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 14th 2010, 03:24 PM
  3. Integration partial fraction
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 10th 2009, 01:34 PM
  4. Partial fraction integration
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 9th 2009, 09:52 AM
  5. Integration a partial fraction
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 8th 2008, 06:07 PM

Search Tags


/mathhelpforum @mathhelpforum