# Line Integral

## Homework Statement

(i) Evaluate

$$\int_C \dfrac{-ydx + xdy}{9x^2 + 16y^2}$$

when C is the ellipse

$$\dfrac{x^2}{16} + \dfrac{y^2}{9} = 1$$

(ii) Use the ans to (i) to evaluate the integral along C' = ellipse:

$$\dfrac{x^2}{25} + \dfrac{y^2}{16} = 1$$

## The Attempt at a Solution

I have done (i) but have no clue about (ii). great thnx for any help.

HallsofIvy
Homework Helper
Okay, what did you get for (i)? I can think of a number of ways that might help you answer (ii) but since you have shown no work at all I don't know which way would be appropriate for you. Do you know Green's Theorem?

got pi/6 for i. didn't use green's for that. the other way is easier. for ii u can't use green's since it would either be too complicated or impossible to integrate. yes i know green's thm. sorry for not showing any work. i just don't know what to do for ii.

HallsofIvy
Homework Helper
That's not at all what I get for (i). And the problem with (ii) is I don't know what theorems or methods you have available. I do notice that the integrand is defined everywhere except at (0,0) which is inside both ellipses.

checked it and still got the same. is it allowed to say 9x^2 + 16y^2 = 144 on that integral? that's something i'm using.

for ii, if u could mention some of the methods u have in mind, i might recognize it as something given in class. thnx

HallsofIvy
My apologies. I just screwed up (1) by copying part of the problem incorrectly. Yes, $\pi/6$ is the correct answer.