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

Answer 1

# ~~ 5.27037 #

The Arc Length of curve #y=f(x)# is calculated using the formula:
# L = int_a^b sqrt(1+(dy/dx)^2) \ dx #
So with #f(x) = 2sinx#, we get:
# dy/dx = 2cosx #

And so the required Arc Length is given by:

# L = int_0^pi sqrt(1+(2cosx)^2) \ dx # # \ \ = int_0^pi sqrt(1+4cos^2x) \ dx #

This integrand does not have an elementary solution

Using Wolfram Alpha this integral evaluates to:

# L ~~ 5.27037 #
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Answer 2

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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