Today we reviewed the process of finding area by evaluating the limit of a Riemann sum. We also reviewed the definite integral sign whose components remind us of the evaluation of a limit of a sum of (heights =f(x) times widths =dx). We then focused on lower and upper sums and defined a function to be "integrable" if the lower and upper sums approach the same limiting value. We then looked closely at a discontinuous function that still managed to be integrable and another function that is not integrable. (see slideshow)
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Today we reviewed the process of finding area by evaluating the limit of a Riemann sum. We also reviewed the definite integral sign whose components remind us of the evaluation of a limit of a sum of (heights =f(x) times widths =dx). We then focused on lower and upper sums and defined a function to be "integrable" if the lower and upper sums approach the same limiting value. We then looked closely at a discontinuous function that still managed to be integrable and another function that is not integrable. (see slideshow)
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