Plotting an integral

[Wes Loewer]

(10-12-2019 07:55 PM)lrdheat Wrote:  I am still a little confused as to why, mathematically, it is incorrect to have everything in terms of X...

[teacher hat on]
If you were to define a function
f(x)=integral from 0 to x of sin(x) dx
then you are using the first x as the limit and the other x's as the variable of integration. To calculate f(3), you substitute 3 in for x and get
f(3) = integral from 0 to 3 of sin(3) d3
which of course is meaningless.

If you instead wrote
f(x)=integral from 0 to x of sin(t) dt
Then f(3)=integral from 0 to 3 of sin(t) dt
The x has the fixed value of 3 while t varies from 0 to 3.

In the function app, if you enter
F1(X)=∫(SIN((π*T^2/2)),T,0,X)
F2(X)=∫(SIN((π*X^2/2)),X,0,X)
and then from Home enter F1(3) you get the correct result of ∫(SIN((π*T^2/2)),T,0,3), but with F2(3) you'll get an error message because it's trying evaluate ∫(SIN((π*3^2/2)),3,0,3)
[teacher hat off]