Reference no: EM13851266
Example 1: let F(x,y) = (xy2,y+x).verify greens theorem for the region bounded by
Y = x2, y=x, (x,y≥0).
![156_1.png](https://secure.expertsmind.com/CMSImages/156_1.png)
Example 2: redo example 2 in the line integrals.evaluate
c∫ x2dx + xy dy
Over the unit square in the diagram below.
![727_2.png](https://secure.expertsmind.com/CMSImages/727_2.png)
Example 3: let f(x,y) = (2y+ex, x+sin(y2))
Evaluate c∫ f.ds where c is the unit circle centred at(0,0) traversed anticlockwise.
![957_3.png](https://secure.expertsmind.com/CMSImages/957_3.png)
.calculation of line integral is too hard ,so use greens theorem.
Example 4: evaluate ∫ f.ds where
F (x,y) = (-y/x2+y2,x/x2+y2)
And c is the curve 3x2+y2 = 1 oriented anticlockwise.
![157_4.png](https://secure.expertsmind.com/CMSImages/157_4.png)
Area of region in xy plane
If c is a simple closed curve that bounds a region D ,than
Area of D = ½ ∫c=∂d xdx-ydx
Example 5 : find the area of region enclosed by
![1419_5.png](https://secure.expertsmind.com/CMSImages/1419_5.png)