Integration 3
2014-05-14 1:49 pm
Find the arc length of the curve defined by y = (x^2)/8 − ln x, where 2 ≤ x ≤ 4. [Answer: [3/2 + ln 2]
回答 (1)
2014-05-14 9:08 pm
✔ 最佳答案
dy/dx = x/4 - 1/x1 + (dy/dx)^2 = 1 + (x/4 - 1/x)^2
= 1 + x^2/16 + 1/x^2 - 1/2
= 1/2 + x^2/16 + 1/x^2
= ( x/4 + 1/x)^2
so sqrt [ 1 + (dy/dx)^2] = (x/4 + 1/x)
Arc length, L = ∫ (x/4 + 1/x) dx = x^2/8 + ln x
when x = 2
L = 1/2 + ln 2
When x = 4
L = 2 + ln 4
So arc length = 2 + ln 4 - 1/2 - ln 2
= 3/2 + ln ( 4/2)
= 3/2 + ln 2.
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