4.9 Arc Length: Quiz

Problem 5

Consider the curve f(x) = xn, between x = 0 and x = 1 and n a positive integer. For any n, f(0) = 0 and f(1) = 1, but the curve has a different shape:

n = 1:

n = 3

n = 10

Find a formula for the trapezoidal approximation for the arc length of f(x) = xn using n trapezoids.

Answers, problem 5

The arc length is given by the integral

The trapezoidal approximation using n trapezoids is

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