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

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

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


    please show me the step by step..
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    Quote Originally Posted by mastermin346 View Post
    A curve has a gradient function of  3x^2-2x+5.Given that the curve passes through the point (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:

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

     = x^3 - x^2 + 5x + C.


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

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

    2 = C.



    So the function is

    f(x) = x^3 - x^2 + 5x + 2.
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