- #1

Zack K

- 166

- 6

- Homework Statement
- State the integral (do NOT evaluate) to compute the arc length between x = 1 and x = 5 for the function ##y=\frac{1}{x^2}## (already done)

How many intervals are required to numerically compute the integral in to an accuracy of ##10^{-3}## using the trapezoidal rule?

- Relevant Equations
- ##L=\int_a^b \sqrt{1+(\frac{dy}{dx})^2}dx##

##E_T\leq\frac{(b-a)^3}{12n^2}[max |f^{(2)}(x)|]##

I got the first part of it down, $$L=\int_1^5 \sqrt{1+(\frac{1}{x^2})}dx$$

I just want to know if it's right to make your ##f(x)=\sqrt{1+\frac{1}{x^2}}## then compute it's second derivative and find it's max value, for the trapezoidal error formula.

I just want to know if it's right to make your ##f(x)=\sqrt{1+\frac{1}{x^2}}## then compute it's second derivative and find it's max value, for the trapezoidal error formula.