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Math Help - Area of a region bounded by graphs

  1. #1
    Junior Member xterminal01's Avatar
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    Area of a region bounded by graphs

    Find the Area of a region bounded by graphs of the function

    x^2+4, y=-x+4 x=2

    I found the integration points to be 0 and 2.
    the f(x)-g(x) i am not sure how to determine which is f(x) and which is g(x)
    I've done the integral (x^2+4)-(-x+4)=> (x^2+x) integrate (X^3/3+X^2/2)dx
    evaluating at 2 => (8/3+2)-(0) = 14/3 is my result?
    Is this correct?
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  2. #2
    MHF Contributor
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    Try this. No pictures.

    x^2 + 4 = 4 - x ==> x^2 + x = 0 ==> x(x+1) = 0 ==> x = 0 or x = -1

    What is important to note is that there is NO solution on (0,2). This is wonderful. It says, since these two guys are continuous, that whichever is on top at all is ALWAYS on top on (0,2). All that is required is to determine which is on top. Try x = 1. This will tell you which is which.

    Note: Please don't get into your head the idea that you need to memorize the formula f(x) - g(x). If you do this, what will you do when the problem statement gives you r(x)? Think about what you are doing and you will not have this problem. Generally, you will want to subtract the lesser area from the greater area. You don't need to memorize a formula to remember that.
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