Question

let f(x)=1/10x^5+1/6x^-3 on[1,2]. find the arc length

Answer 1

$L = \int_a^b \sqrt {1+ (f^\prime(x))^2} dx;$

$f^\prime(x) = 0.5*x^4 - 0.5*x^{-4};$

$L = \int_1^2 \sqrt {1+ (0.5*x^4 - 0.5*x^{-4})^2}dx = \int_1^2 \sqrt {0.5+ 0.25*x^8 + 0.25*x^{-8}}dx$

$L = \frac{3x ^ 8 - 5}{30x^3} \mid_1^2 = 763 / 20 + 2 / 30 \approx 3.2458$

ANSWER: 3.2458