# Area, Volume, and Arc Length

### Example 1

Find an integral expression for the length of the curve *f*(*x*) = ln *x* on [2,4].

### Example 2

(a) Find an integral expression for the length of the curve *f*(*x*) = 1 – *x*^{2} on [-1,1].

(b) Use a calculator to evaluate your integral. Determine if your answer is reasonable by comparing the curve to the upper half of the unit circle.

### Example 3

(a) Write an integral expression for the length of the curve *f*(*x*) = -*x* on [-1,1].

(b) Evaluate your integral.

(c) Find the length of this curve without using calculus. Does your answer agree with the answer you found using the integral?