- #1
bugatti79
- 794
- 1
Homework Statement
Evaluate this integral directly
Homework Equations
[itex]\int cos x sin y dx +sin x cos y dy[/itex] on vertices (0,0), (3,3) and (0,3) for a triangle
The Attempt at a Solution
Does this have to evaluated parametrically using [itex]r(t)=(1-t)r_0+tr_1[/itex] for [itex]0 \le t\le 1[/itex]
or can I just proceed evaluating each line segment in a counter clockwise manner starting with the vertices:
from (0,0) t (3,3) which gives the line y=x hence dy=dx, substituting in the above
[itex] \displaystyle I_{ab} = \int_0^3 (cos x sin x + sin x cos x ) dx = \int_0^3 sin 2x dx[/itex]...?