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Objective competence and experience in the following subjects: Photography/lenses, fitness, electric guitar, golf, tennis, trading stocks, nutrition, chess, programming, and wine tasting. PM me for information on any of these topics.


Dec
14
comment Don't see the point of the Fundamental Theorem of Calculus.
I am the OP. I am truly grateful and humbled by knowledge shared by this collective brain trust. In the next few days, I am going to do this thread justice and read everything when I can be alone for a few hours next week. Thank you again for this.
Dec
14
comment Don't see the point of the Fundamental Theorem of Calculus.
I am the OP. I am truly grateful and humbled by knowledge shared by this collective brain trust. In the next few days, I am going to do this thread justice and read everything when I can be alone for a few hours next week. Thank you again for this.
Dec
14
comment Don't see the point of the Fundamental Theorem of Calculus.
I am the OP. I am truly grateful and humbled by knowledge shared by this collective brain trust. In the next few days, I am going to do this thread justice and read everything when I can be alone for a few hours next week. Thank you again for this.
Dec
12
awarded  Good Question
Dec
12
revised What does this FTC scenario actually represent?
edited body
Dec
12
comment What does this FTC scenario actually represent?
Fixed it. Got an answer for my actual question?
Dec
11
awarded  Notable Question
Dec
11
awarded  Popular Question
Dec
11
awarded  Nice Question
Dec
11
revised What does this FTC scenario actually represent?
added 86 characters in body
Dec
11
asked What does this FTC scenario actually represent?
Dec
11
comment Don't see the point of the Fundamental Theorem of Calculus.
That 2nd part is how I tied together the big 3: anti-derivative (integral) = area under a curve = total displacement. However, this made the assumption that one already has defined the idea of an integral being the anti-derivative. Which is how I knew to use $f(x)=x^2$ and $f(x)=2x$
Dec
11
comment Don't see the point of the Fundamental Theorem of Calculus.
David, thanks for your response. I have informally understood definite integrals by calculating total distance traveled on a (constant) position graph, and noticing that the total distance traveled equaled the area under this rate curve (eg: 3 hours at a constant 50 mph = 150 total miles, which also happens to match the area (3 x 50 = 150). So, the area under the rate graph equals the total displacement. Then, I took an actual example like $f(x)=x^2$ and calculated displacement on [2,5] via $\frac{f(5)-f(2)}{5-2}$ and then noticing that the area under $f(x)=2x$ on [2,5] matches that.
Dec
11
revised Don't see the point of the Fundamental Theorem of Calculus.
added 22 characters in body; edited title
Dec
11
asked Don't see the point of the Fundamental Theorem of Calculus.
Dec
6
comment How to link definite integral $\leftrightarrow$ Area under curve $\leftrightarrow$ total displacement
But how is the sum of rectangle areas as deltaX -> 0 turned into the definite integral?
Dec
5
asked How to link definite integral $\leftrightarrow$ Area under curve $\leftrightarrow$ total displacement
Dec
3
revised Car's airbag deployment system. Let's discuss the math!
added 5 characters in body
Dec
2
accepted Car's airbag deployment system. Let's discuss the math!
Dec
2
comment Car's airbag deployment system. Let's discuss the math!
Gotcha. For now, I just want to be 1 step closer to a viable hypothesis on the airbag math. Before today, I assumed it was done by little elves and unicorns in the bumper. Now, I think the "ACU calculates real time negative rate of change threshold" hypothesis might be more accurate, at least for the context of driving into a brick wall.