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Welcome to March Calculus Madness!
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What is the arc length of y = sin x and y = cos x from x = 0 to x = 2 * π
The arc length of y(x) is calculated by:
∫ √(1 + (dy/dx)^2) dx for x = a to x = b
For y(x) = sin x, dy/dx = cos x, (dy/dx)^2 = cos^2 x
Arc length of y = sin x from x = 0 to x = 2*π
∫ √(1 + cos^2 x) dx for x = 0 to x = 2*π ≈ 7.64039557806
Likewise, for y(x) = cos x, dy/dx = -sin x, (dy/dx)^2 = sin^2 x
∫ √(1 + sin^2 x) dx for x = 0 to x = 2*π ≈ 7.64039557806
Yes, the arc lengths are the approximately the same.
Eddie
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