Arclentgh of y= sqrt(x-x^2) + arccos(sqrtx)

In this video, I showed how to find the length of an arc if no bounds of integration are given for asum of functions

[@MathFromAlphaToOmega]

I thought I'd seen most of the curves with nice arc lengths, but this is a new one!

[@adamkucera9094]

Me too.

[@blackovich]

You are a good-looking guy. I'm sorry, I had to type that on a math channel.

[@florianbasier]

Nothing critical but your explanations on the domains were a bit unprecise to say the least. the "a quadratic is less than 0 between its two roots" is true in this case, but only because the coefficient of x2 is positive. if you have a quadratic with a negative leading coefficient, it is negative outside of the roots. The explanation for the second domain is as well lacking discipline. You can't just "change the -1 to 0". Since you are working in R, you can say that 0

[@benchapple1583]

This is not a criticism, rather it's a question. Why do you favour the form "y = whatever" as opposed to "f(x) = whatever"? I have always seen this written as f(x) or g(x) etc. and their derivatives as f'(x) g''(x) etc.

[@PrimeNewtons]

Just takes less space on my small board. I personally prefer f(x)

[@benchapple1583]

@@PrimeNewtons Thanks for taking the time to answer.

[@aminimam5118]

y=5-x/2 and the other side is 5-x (5-x/2)^2+(5-x)^2=25 it is a straightforward problem,

[@dirklutz2818]

Terrific!

[@vitotozzi1972]

Fantastic job!

[@pauljackson3491]

What is the name of the fancy 'L' the integral is equal to? Also, you can't use squares in greater or lesser than. -3 < 2 but it isn't true that (-3)^2 < (2)^2 = 9 < 4

[@rogerkearns8094]

1. I call it 'curly ell'. 2. Didn't he say that, about comparing squares? I thought he did.

[@justabunga1]

Here is another example of y=(sin(x))^2. If you look at the function as y=sin(x), it ranges between -1 and 1. When you square the sine function, the range has to be in between 0 and 1 because (-1)^2=1, we cannot have some values that are less than 0 in that range. That's why we have to have values that are between 0 and 1.

[@surendrakverma555]

Thanks Sir 👍