Question

help plz !
will fan+ medal ｡◕ ‿ ◕｡
what kind of curves , i can solve
there length using

Answer 1

\(\color{blue}{\Huge L:=\int\limits_{a}^{b} r'(t)^2 dt}\)

Answer 2

arc length formula doesnt look right

Answer 3

\(L = \int \limits_a^b | r'(t)| dt\)

Answer 4

\(L = \int \limits_a^b | r'(t)| dt = \int \limits_a^b \sqrt{x(t)^2 + y(t)^2 + z(t)^2 } dt\)

Answer 5

this works for any kind of curves that are continuuous and differentiable

Answer 6

you are right , it should be
\(\color{blue}{\Huge L:=\int\limits_{a}^{b} \sqrt {r'(t).r'(t)} dt}\)

Answer 7

sometime evaluating integral might not be possible, in which case you need to approximate... but still you would use the same formula

Answer 8

but i tried for more than curve it dint work unless for circle and simple lines
otherwise evaluating integral looks not possible

Answer 9

so, its in general but

Answer 10

not each time i reach the exact right ?

Answer 11

well it make sense !
so there is specifies type of curves i can get an exact solution ?!

Answer 12

well thx @rational for brainstorming !

Answer 13

we cannot integrate every curve by hand

Answer 14

that should be understood :)
we can differentiate anything. but we cannot integrate everything

Answer 15

ok ಠ_ಠ

Answer 16

but still the given formula wont fail, u wil use the same formula... but use computation to approximate the integral instead

Answer 17

it well need more works lol