# How do you find the arc length of the curve #y=2sinx# over the interval [0,2pi]?

# ~~ 5.27037 #

And so the required Arc Length is given by:

This integrand does not have an elementary solution

Using Wolfram Alpha this integral evaluates to:

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To find the arc length of the curve y = 2sin(x) over the interval [0, 2π], you can use the formula for arc length of a curve given by:

Arc Length = ∫[a,b] √(1 + (dy/dx)^2) dx

First, find dy/dx by differentiating y = 2sin(x) with respect to x. Then, substitute the expression for dy/dx into the arc length formula. Integrate the resulting expression over the interval [0, 2π].

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