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TordtheMan982
29.10.2019 •
Mathematics
Find the arc length function for the curve with starting point (0,1).
y=sin−1x+√1−x2
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Ответ:
1 + (dy/dx)^2 = 1 + (1 - x)^2/(1 - x^2) = [(1 - x^2) + (1 - x)^2]/(1 - x^2) = (1 - x^2 + 1 - 2x + x^2)/(1 - x^2) = (2 - 2x)/(1 - x^2) = 2(1 - x)/[(1 + x)(1 - x)] = 2/(1 + x)
ds = √(1 + (dy/dx)^2 = √(2/(1 + x)) = √2/√(1 + x) dx
L = √2 ∫ dx/√(1 + x) {0, 1} = √2 ∫ (1 + x)^(-1/2) dx = 2√2 √(1 + x) {0, 1} = 2√2 (√2 - 1) = 4 - 2√2 ≈ 1.1716
The arc length would be 1.1716 units.
I hope my answer has come to your help. Thank you for posting your question here in .
Ответ: