# Find Arc Length Using Trapezoids

1. Dec 4, 2005

### nyyfan0729

Using trapezoids and N=4, find the length of the arc of the curve y=(1/3)x^3 from (0,0) to (1,1/3).

2. Dec 5, 2005

### HallsofIvy

Staff Emeritus
Of course, $\frac{dy}{dx}= x^2$ so the length of the curve from x= 0 to x= 1 is
$$\int_0^1 \sqrt{1+ x^4}dx$$

By "Using trapezoids" do you mean use the trapezoid rule to numerically integrate that?