how can I find length of line?

[plucky cliff]

In calculus 1, I learned how to find slope of function and area of function
but I never learn how to calculate length of line, but why? is there any theorem to find length of line of function?

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[ionic zenith]

Pythagorean theorem

$$l = \sqrt{(\Delta x)^2+(\Delta y)^2}$$

[kind folio]

Adler

[plucky cliff]

oh so I need to use pytgagorean and decrease it very small?

[ionic zenith]

no

$$\Delta x = x_2 - x_1$$

[kind folio]

Adler

[plucky cliff]

but how can I applied to find length of f(x) ?

[ionic zenith]

It is the difference between the points

[plucky cliff]

when f(x) isn't straight line

[ionic zenith]

When it is not a line but a curve, you use integrals, and now a very small delta x

[plucky cliff]

ohh

thanks

[ionic zenith]

It's called arc length, I think.

[plucky cliff]

.close