Question

Given the equation xy = 2, set up an integral to find the length of path from x = a to x = b and enter the integrand below.

I did the integral from b to a and set it equal to the sqrt(1+4/x^4), because I found y to equal 2/x and the derivative to be -2/x^2, but I think I am solving the problem wrong.

Answer 1

y = 2/x (The is the integrand). The derivative is -2/x^2
When calculating the length of a line, you have to integrate sqrt[1 + (dy/dx)^2], which in this case is
sqrt[1 + 4/x^4]. That function is the integrand.

Your last step is wrong.
The line length from a to b is the difference in the values of the INTEGRAL of sqrt[1 + 4/x^4] dx at the two end points.

I don't have a clue abut how to integrate that function, but they are only asking you to set up the integral anyway.