Question

Write down definite integrals to express the given geometric quantities :

The arc length of the curve formed by$y=f\left(x\right)$on$\left[a,b\right]$.

Short answer

Arc length of$f\left(x\right)$on$\left[a,b\right]$$={\int }_a^b\sqrt{1+{\left(f\text{'}\left(x\right)\right)}^2}dx$

Step-by-step solution

Given Information : 

Given that to assume that $f\left(x\right)$is continuous and differentiable, with a continuous derivative.

Definite integral formula for arc length :

The arc length of $f\left(x\right)$from $x=a$to $x=b$can be represented as,

Arc Length$={\int }_a^b\sqrt{1+{\left(f\text{'}\left(x\right)\right)}^2}dx$