8.1 Arc Length Review

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5 Terms

1
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dℓ =

sqrt(dx² +dy²)

2
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for curve C defined by y = f(x), a<= x <=b then

dℓ = sqrt(dx²)sqrt(1+(dy/dx)²)

3
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for curve C defined by y = f(x), a<= x <=b then (SIMPLIFIED)

ℓ = int (bounds a, b)(sqrt(1+(f’(x))²)dx)

4
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for curve C defined by x = g(y), c<= x <=d then

dℓ = sqrt(dy²)sqrt(1+(dx/dy)²)

5
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for curve C defined by x = g(y), c<= x <=d then (SIMPLIFIED)

ℓ = int (bounds c, d)(sqrt(1+(g’(y))²)dy)