Calculating Line Integral of (x^3-y^3)dx +(x^3+y^3)dy

[scarebyte]

1.find the line integral of
(x^3-y^3)dx +(x^3+y^3)dy over r, where r is the boundary of the
region limited by x^2+y^2=1 and x^2+y^2=9

Homework Equations

3.
i found that the
line integral over the curve x^2+y^2=1 is 3*Pi/2
and the double integral of the region limited by x^2+y^2=1 and x^2+y^2=9 is 120*Pi
so the answer would be 120*Pi + 3*Pi/2 ?

 

[Dick]

The question is not very clear. The region between x^2+y^2=1 and x^2+y^2=9 consists of two curves that aren't connected. A proper question would specify the direction for each part of the contour. 120*pi is correct if you make a certain assumption about the direction of each contour. Whoever is giving you these questions should really work on phrasing them better.