Calculating the arc length of an ellipse

[jaunty agate]

I know I'm effectively asking for a calculus crash course, but I only ever studied up to trig and I'm at a loss on how to do this.

Given these variables I'm trying to calculate the arc length of x assuming it's part of a perfect ellipse with the given information. How would I go about doing that?

[jaunty agate]

I know the semiminor axis (at least I think that's what it's called) should be like 1.5 based on the information given, but I'm not entirely sure what to do with it. I heard something about calculating "T" for an "elliptic integral" but I'm not entirely sure what those are or how to calculate them. I tried doing what I understood to be the steps in this webpost I found, but I keep getting the wrong answer.
https://math.stackexchange.com/questions/433094/how-to-determine-the-arc-length-of-ellipse

[minor wharf]

x(t) = acosθ
y(t) = bcosθ

[jaunty agate]

Yeah, I saw that, but I'm not entirely sure how to calculate those or use them to calculate the arc length

[neat sandal]

adonhs

[jaunty agate]

I have no idea what most of this means

[minor wharf]

a and b are the length and width of the ellipse

[jaunty agate]

And I'm guessing theta is the angle between the start of the arc and the end of the arc, but I have no clue what the rest of it is or what it even wants me to do with it

[minor wharf]

b = 3 for a you would need to figure out the width

using pythagoras

[jaunty agate]

You mean the other radius? Because it was really close to 1.5 last I checked

[minor wharf]

x' is the derivative of x(θ)
y' is the derivative of y(θ)

and additinally both are being squared

[jaunty agate]

I don't know what to do with those values, though

[jaunty agate]

And I'm not sure what that means

[minor wharf]

I figured it to be 2

[jaunty agate]

It might be. I probably erroneously assumed a right triangle

[minor wharf]

It's a parameterization

[jaunty agate]

I don't know what that means either

[minor wharf]

There is an alternative without it but you will need the eclipse equation

[jaunty agate]

The x2/a2 + y2/b2 = 1 one?

[neat sandal]

adonhs

[jaunty agate]

The bottom equation still makes no sense to me

[minor wharf]

Since y = f(x) you would have to solve the eclipse equation for y and then choose the + or - version depending on the bounds and differentiate it.

[minor wharf]

Yea if you want a proof or the "why" do some self research

[jaunty agate]

I don't know what the equation is even asking me to do

[minor wharf]

You are integrating

Thats all

[jaunty agate]

Yeah. I don't know what that is

[minor wharf]

Oh

You mentioned elliptic integral

So I assumed you knew integration

[jaunty agate]

I mentioned that being a term I've seen, but had no understanding of

[minor wharf]

It's a symbol

[jaunty agate]

I don't know what kind of operation it's asking for

[minor wharf]

Why dont you use an online calculator then?

[minor wharf]

Do you know differentiation?

[jaunty agate]

I don't know what that is either

[minor wharf]

Well

You really are asking for a crash course

[jaunty agate]

Yeah, I'm aware