F bar of x5/30/2023 ![]() ![]() So just by the fundamental theorem of calculus (basically the definition of what an integral is), evaluating a definite integral means to take the antiderivative of the function and subtract from the upper limit from the lower limit, and thats a measure of how much the original function changed. Because given some interval, h(b) - h(a) = a 2 + 3a + C - (b 2 +3b +C) = a 2 +3a - b 2 - 3b, the constant just ends up cancelling and this makes sense because if were measuring change, constants do not. finding the "h(x)") gives a nonunique solution, the amount that these anti derivatives Change on an interval is equal. So, while integrating a function (taking the anti derivative, i.e. So given only that some derivative h'(x) = 2x + 3, you know the original function h(x) could be x 2 + 3x -2, or x 2 +3x + 5, and so on, in fact, any function of the form h(x) = x 2 + 3x + C, where C is some constant. But note that g(x) = x 2 + 3x +5 would have the exact same derivative. For example, for the function f(x) = x 2 +3x -2, the derivative is f'(x) = 2x + 3. ![]() Ok, my question is, why does that notation exist, and why subtract? I'm assuming it is related to the whole 1/(b-a) multiplier for determining average value of the function, but I haven't seen it explained, and I can't figure out the right search terms for google because I don't know what that operator is actually called.īasically I'm looking for a simple tutorial (here, online, etc) on how/when/why to use that notation.ĭerivatives represent how much a function is changing, and each function has a unique derivative, but each derivative only has a partially unique "parent" function in the sense that it may differ by a constant. Also, I gathered from watching PatrickJMT's video (and a KhanAcademy video as well) on integral average values that in this case the notation means to evaluate the integral at both ends and apparently subtract the lower integral from the upper integral. I've seen it online occasionally with derivatives (usually in physics examples) with (only) the number on the bottom and the meaning to evaluate the derivative at that number, which was easy enough to figure out. By the calculation of the taxpayer, the amount due was 10K per. By IRS math, that would be 10K x the 272 accounts listed on the five reports, or 2.72 million. The IRS view is that the penalty for a nonwillful late filing of each report is 10,000 per account. What does F-BAR mean as an abbreviation 5 popular meanings of F-BAR abbreviation: 8 Categories. The legal argument arose over the application of penalties for late-filing an FBAR. Most common F-BAR abbreviation full forms updated in March 2023. Nothing I've seen in my text or elsewhere seems to explain what this notation actually means. List of 5 best F-BAR meaning forms based on popularity. This is from an average value integral step I copied from a PatrickJMT video on average value. While trying to read up a bit on average value using integrals beyond the single example my book has, I run repeatedly into this type of notation: ![]()
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