Trying to teach myself calculus. Explain to me why I can't find the area under this hyperbola, length of the thing, what not, using the perpendiculars that I spent 5 hours in Desmos doing addition of 1/sqrt(2) and 4/sqrt(5) and a bunch of other shit.
>>7941695
because you'll be approximating the segments of the curve as straight lines?
>>7941698
Then what is this meme staircase method I keep seeing? Is that only for repeating series? Define things, please?
>>7941695
what's the curve's ecuation?
>>7941695
stop trying to reinvent the wheel and learn how to use the definite integral
>>7941700
oh, you meant if you had infinitely many of those perpendiculars infinitely close together? you could do that, but the calculation would probably be messier than a standard integral
>>7941709
The idea that originated the curve is that there would be a segment with a length of sqrt(1), at the angle of 1(which is 45), which would make the first segment coordinates (1/sqrt(2) - 0, 1/sqrt(2) - 0) so that a circle with a radius of 1 would have that line as its radius. The rest of the segments are literally addition, segment 1 plus segment 2 is approximately a radius of 3, it cuts short because the hypotenuse cannot be the same length of a triangle as the base, but if you removed segment 1 from segment 1 + segment 2, you would have an absolute radius of two.
The thing with the perpendiculars is fucking insane.
Here is a link to the graph: https://www.desmos.com/calculator/njgfolvwjo
>>7941738
>https://www.desmos.com/calculator/njgfolvwjo
change the last o to a 0.
>>7941747
idk how you came up with those points or if you even had an equation to start with but here is a trend-line as close to the points as possible
you could probably express the points as an infinite series for better accuracy but i've wasted enough time on this as it is
