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Math Help - Area bounded by curves

  1. #1
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    Area bounded by curves

    Show that the area of the region bounded by the curve y= x^2 +2x -1 and the curve y= -x^2 +2x +7 is 64/3 units^2.

    After I sketched the graph, then what should i do?
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  2. #2
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    Re: Area bounded by curves

    Hi Alexander9408: I assume you already know that the area under one curve is the integral from the start point to the end point. Well, the area between two curves is the integral of the outer curve minus the inner curve. By "outer" curve, I mean "furthest from the x axis." Look at your sketch and decide which is the outer curve and then subtract the formula for the inner curve. Now you have what you should integrate. To get your upper and lower bound for integration, you have to do a little algebra to find out where the two curves intersect. Good luck!
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