Posted by Katelyn on Friday, March 13, 2009 at 12:01am.
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.

Calculus  drwls, Friday, March 13, 2009 at 8:13am
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.
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