mighty pecan
Hello everyone. I made an integral approximation in Desmos just for fun. It shows how increasing n makes the summation more accurate for estimating the integral of x from 0 to 1. The higher the n, the closer it gets to the true value. Any ideas for similar projects or improvements?
Here is the link: https://www.desmos.com/calculator/1c7hurfegn
nova path
this is just n+1 / 2n, I'm pretty sure
mighty pecan
yea thats true
nova path
which is the same as 1/2 + 1/2n
the integral from 0 to 1 of f(x) = x is just 0.5 - since 1/2n is the error, it makes sense why a bigger n makes the error smaller. as n approaches infinity, 1/2n approaches 0, bringing you closer to 0.5 (or the area under the function)
mighty pecan
which is the same as 1/2 + 1/2n
the integral from 0 to 1 of f(x) = x is just 0.5...
but the point is to aproximate the integral so it should be kept a summation that does this job
glossy osprey
but the point is to aproximate the integral so it should be kept a summation tha...
Just use the Riemann integral limit formula lol
mighty pecan
why make it more complex
mighty pecan
well listen
we get the aproximmation of the integral
through summations
the easy way
glossy osprey
um
mighty pecan
glossy osprey
this is easy
mighty pecan
this is simple
glossy osprey
?
mighty pecan
simpler
glossy osprey
not really ?
mighty pecan
no need to calculate limits
glossy osprey
that is a limit
mighty pecan
its still the same thing
glossy osprey
no need to calculate limits
you're taking the limit as n goes to infinity though
mighty pecan
the whole point of this
is to show how increasing
the number of strips
gets it more accurate
glossy osprey
yes
mighty pecan
we dont want accuracy
mighty pecan
we want to show how its achieved
glossy osprey
that is what the formula does
it has n strips and increases n
$\int_{a}^{b}f(x)dx=\lim_{n\to\infty}\sum_{i=1}^{n}\frac{b-a}{n}f(a+i\frac{b-a}{n})$
scenic sunBOT
Coffey 2.0
glossy osprey
a+i(b-a)/n is the value of f at the nth strip
glossy osprey
a+i(b-a)/n is the value of f at the nth strip
aka the height
(b-a)/n is the width
so that's the area
glossy osprey
yes, I was too
glossy osprey
me too