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Area between a function and its tangent

  1. Sep 22, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the area of the region bounded by the graph of f(x) = 4x^2, the tangent line to this graph at P(2, f(2)), and the x-axis

    2. Relevant equations

    Integral of [f(x)-g(x) dx]

    3. The attempt at a solution
    I first tried to find the equation for the tangent line
    The derivative of 4x^2 = 8x, subsituting x=2 into the equation I got 16 [slope]
    the equation then turned out to be y-2 = 16 (x-2) --> y = 16x-30
    I then subtracted this tangent equation from 4x^2 then integrate, but I wasn't able to get the right answer.
    Please show me how...thank you!
  2. jcsd
  3. Sep 22, 2008 #2


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    Why did you have y - 2 = 16(x - 2)? If I plug in x = 2 I think it is not a tangent line...
  4. Sep 22, 2008 #3


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    Hi Momentum09! :smile:

    I'll just add to what CompuChip :smile: says …

    why not just integrate under the parabola in the usual way, and then subtract the area of the triangle using half-base-times-height? :wink:
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