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.

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