length of an arc curve

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lvyral93

Mathematics

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Explanation & Answer

dx/dy = y² - 1/(4y²) 

1 + (y² - 1/(4y²))² = (16y^8 + 8y⁴ + 1)/(16y⁴) = (4y⁴ + 1)²/(4y²)² 

√(1 + (dx/dy)²) = √((4y⁴ + 1)²/(4y²)²) = (4y⁴ + 1)/(4y²) = y² + 1/(4y²) 

₃ 
∫(y² + 1/(4y²)) dy = [y³/3 - 1/(4y)]₁³ = 9 - 1/12 - 1/3 + 1/4 = 53/6 ≈ 8.83 
¹


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