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Area, Volume, and Arc Length

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 – x2 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?

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