Results 1 to 2 of 2

Thread: area under a curve as the limit of a sum of areas

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    202

    area under a curve as the limit of a sum of areas

    A curve has a gradient function of $\displaystyle 3x^2-2x+5$.Given that the curve passes through the point $\displaystyle (0,2)$,find the equation of the curve.


    please show me the step by step..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by mastermin346 View Post
    A curve has a gradient function of $\displaystyle 3x^2-2x+5$.Given that the curve passes through the point $\displaystyle (0,2)$,find the equation of the curve.


    please show me the step by step..
    This isn't finding an area, it's finding an antiderivative...

    The function you are looking for is:

    $\displaystyle f(x) = \int{3x^2 - 2x + 5\,dx}$

    $\displaystyle = x^3 - x^2 + 5x + C$.


    Now using the fact that $\displaystyle (0, 2)$ lies on the curve:

    $\displaystyle 2 = 0^3 - 0^2 + 5\cdot 0 + C$

    $\displaystyle 2 = C$.



    So the function is

    $\displaystyle f(x) = x^3 - x^2 + 5x + 2$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Jul 3rd 2010, 10:40 PM
  2. area between this curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 13th 2010, 02:36 PM
  3. Replies: 0
    Last Post: Jun 18th 2008, 03:51 PM
  4. Area Under a Curve
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Nov 11th 2007, 04:01 PM
  5. Replies: 1
    Last Post: Jul 22nd 2007, 07:33 PM

Search Tags


/mathhelpforum @mathhelpforum