What is the arclength of f(x)=x^2e^(1/x)f(x)=x2e1x on x in [1,2]x[1,2]?

1 Answer
Jul 14, 2018

approx 16.431616.4316

Explanation:

We are using the Formula

int_a^bsqrt(1+(f'(x))^2)dx
Calculating f'(x)

f'(x)=2xe^(1/x)+x^2*e^(1/x)(-1/x^2)
simplifying we get

f'(x)=e^(1/x)(2x-1)
so we have to compute

int_1^2sqrt(1+(e^(1/x)(2x-1))^2)dx

This integral can not expressed by the known elementary functions.

By a numerical method we get approx 16.4316