📝 Finding Arc Length By Numerical Methods

Q1. A curve is given by \(y=\sqrt{x}\) on \([1,4]\). Using the trapezoidal rule with \(n=3\) subintervals, what is the approximate arc length?

💡 Difficulty: easy | ✅ Correct: C

Q2. For the parametric curve \(x=t^2,\;y=t^3\) on \(t\in[0,2]\), which numerical method gives the most accurate estimate of arc length using only two subintervals?

💡 Difficulty: medium | ✅ Correct: C

Q3. For the function \(y=e^{x^2}\) on \([0,1]\), which numerical method guarantees the smallest upper bound on the error when using three subintervals?

💡 Difficulty: hard | ✅ Correct: D