Basic Mathematics20795 marksNumerical: arc length of curveArc length of curves
Define arc-length of the curve. Find the length of the curve y = left(fracx2right)frac23 from x = 0 to x = 2. [1+4]
Define arc-length of the curve. Find the length of the curve $y = \left(\frac{x}{2}\right)^{\frac{2}{3}}$ from $x = 0$ to $x = 2$. [1+4]
- Curve: $y = \left(\dfrac{x}{2}\right)^{2/3}$ - Limits: from $x=0$ to $x=2$ The arc-length of a curve is the length of the curve measured along it between two given points. For a smooth curve $y=f(x)$ from $x=a$ to $x=b$: $$L = \inta^b \sqrt{1+\left(\frac{dy}{dx}\right)^2},dx$$ Step 1: Compute ...