Q. 5 - Calculus

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 $\left[a,b\right]$.

Step-by-Step Solution

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 1: Given Information :

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

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