1.Description
The line integral of arc length, also known as the first kind of line integral, derives its physical significance from calculating the mass of a spatial curve given a density function.
2.Programming Example
To compute the first kind of line integral, calculate∫xyds along the curveL, where the curveL isx²+y²=a² in the second quadrant.
Program:
syms a x y
y=sqrt(a^2-x^2)
f=x*y
g=sqrt(1+diff(y,x)^2)
int(f*g,x,-a,0)
Execution Result:
y =
(a^2 – x^2)^(1/2)
f =
x*(a^2 – x^2)^(1/2)
g =
(x^2/(a^2 – x^2) + 1)^(1/2)
ans =
-a^3/2
[Reference Video Explanation 13.16]
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