I cant seem to get this problem right:
from what i understand, you solve these with respect to x and y by parameterizing the curve which gets me for the first part r(t)=<sqrt(2)t,0> and r'(t)=<sqrt(2),0>. But when i plug it in as (0) and sqrt(2) for y and dx respectively i only get 0 when i evaluate my integral. the correct answer for C1 should be 1/2, What am i doing wrong? also, i havent even tried the 2nd or 3rd line integrals yet, but would the arc from the circle be integrated from 0 to pi? Thanks.
Along the line from, to the integration would be zero. But along the line which joins the points (0,0) and (1,1);
This may be the result stated.
When you integrate along the arc, you have to consider limiting points of the arc. In this case the x coordinate varies from, . Hence write the integral interms of x and substitute these boundry points,
If you want to convert this into polar coordinates, substitute the relevant transformations. Hope you would be able to continue.
If you looked at it from the big picture and did your research, it's known that Green's Theorem can be used to find the area of a region enclosed by a curve C:
So if you if you do the line integral right, your answer should be negative that of the area of the enclosed region. If you do it right the answer for a) is