What is the arc length of f(x)= xsqrt(x^3-x+2) f(x)=xx3x+2 on x in [1,2] x[1,2]?

1 Answer
Jul 12, 2018

approx 4.37124.3712

Explanation:

We are using the formual
\int_a^bsqrt(1+f'(x)^2)dx

by the product and the chain rule we get

f'(x)=sqrt(x^3-x+2)+x*1/2*(x^3-x+2)^(-1/2)*(3x^2-1)

this is

f'(x)=(2*(x^3-x+2)+3x^3-x)/(2sqrt(x^3-x+2))

simplifying we get

f'(x)=(5x^3-3x+4)/(2sqrt(x^3-x+2))
and we have to integrate

int_1^2sqrt(1+((5x^3-3x+4)/(2sqrt(x^3-x+2)))^2)dx
By a numerical method we get 4.3712