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

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

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Prime Newtons

4 ай бұрын

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

Пікірлер: 14

@MathFromAlphaToOmega 4 ай бұрын

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

@adamkucera9094 4 ай бұрын

Me too.

@blackovich 4 ай бұрын

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

@dirklutz2818 4 ай бұрын

Terrific!

@vitotozzi1972 4 ай бұрын

Fantastic job!

@benchapple1583 4 ай бұрын

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 4 ай бұрын

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

@benchapple1583 4 ай бұрын

@@PrimeNewtons Thanks for taking the time to answer.

@surendrakverma555 4 ай бұрын

Thanks Sir 👍

@florianbasier 4 ай бұрын

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

@pauljackson3491 4 ай бұрын

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 4 ай бұрын

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

@justabunga1 4 ай бұрын

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.