Transcription of AREA UNDER A CURVE - swl.k12.oh.us
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AREA UNDER A CURVE - swl.k12.oh.us
AREA UNDER A CURVE . The two big ideas in calculus are the tangent line problem and the area problem. In the tangent line problem, you saw how the limit process could be applied to the slope of a line to find the slope of a general CURVE . A second classic problem in calculus is in finding the area of a plane region that is bounded by the graphs of functions. In this case, the limit process is applied to the area of a rectangle to find the area of a general region. A basic overview of areas as limits. In the limit of rectangles approach, we take the area UNDER a CURVE y = f (x) above the interval [a , b] by approximating a collection of inscribed or circumscribed rectangles is such a way that the more rectangles used, the better the approximation. Finally, the number of rectangles is increased without limit and, bingo, we get the area! Now known as integration. Specifically, we are interested in finding the area A of a region bounded by the x axis, the graph of a nonnegative function y = f (x) defined on some interval [a, b].
AREA UNDER A CURVE The two big ideas in calculus are the tangent line problem and the area problem. In the tangent line problem, you saw how the limit process could be applied to the slope of a line to find the slope of a general curve. A second classic
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