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Calculus2.3 - Section 6.4 Arc Length Elementary geometry...

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Section 6.4: Arc Length
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Elementary geometry doesn’t help to find the length of a curve that wiggles like this. So, let’s break it into pieces we can work with.
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Arc Length: 2 2 2 x s y y x 2 2 s y x 2 2 2 1 x x y 2 1 y x x : y dy Idea x dx * Reason MVT '( ) k dy f x dx 2 1 ' b a f x dx
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f (x) = sinx, 0 x 2 0 1 cos x dx
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2 f (x) = x on [0,3] 3 2 0 1 2 x dx Or, f (y) = on [0,9]
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