Question

Green's Theorem Verification
Check My Solution, somewhere there is an error, I should either get both answer as 5/3 or both as -8/3

Answer 1

@ganeshie8
@SithsAndGiggles

Answer 2

so they both should come out as 5/3.

when you did the left side you forgot the two sides of the triangle

Answer 3

remember to go counter clockwise.

the vertical is :
dx = 0 , x = 0
\[\int\limits_{1}^{0}4ydy\]
which is -2.

the horizontal is :
dy = 0 , y = 0
\[\int\limits_{0}^{1}3x^2dx\]
whici is +1

and the part that you did should be +8/3 (because we go counter clockwise)

so

8/3 -2 + 1 = 5/3

Answer 4

not so sure about evaluating line integral

you considered vertical and horizontal, lines too, in addition to what i considered only
x+y=1 line, right ?

Answer 5

correct

Answer 6

thank you!
got it :D

Answer 7

great yw