How to Integrate Along Curve C_1?

[Ted123]

Homework Statement

[PLAIN]http://img580.imageshack.us/img580/9506/linegu.jpg

The Attempt at a Solution

Parametrising the curve C_1 as follows:

{\bf p}(t) = (1-t)(1,4) + t(3,3) = (1+2t,4-t)


{\bf p}'(t) = (2,-1)

So \int_{C_1} = \bigg\{ \sqrt{\frac{y}{x}} \frac{dx}{dt} + \sqrt{\frac{x}{y}} \frac{dy}{dt} \bigg\} \;dt = \int^1_0 \bigg\{ 2\sqrt{\frac{4-t}{1+2t}} - \sqrt{\frac{1+2t}{4-t}} \bigg\} \;dt

How do I do this integration?

 

[lanedance]

i would attempt to rationalise the integrands