## Trending News

Promoted

# Let C be the positively oriented square with vertices (0,0), (2,0), (2,2), (0,2). Use Green's Theorem to find∫C4y2xdx+3x2ydy.?

### 1 Answer

Relevance

- husoskiLv 75 months agoFavorite Answer
Green says: ∮_C (u dx + v dy) = ∫∫_R (∂v/∂x - ∂u/∂y) dx dy.

You have u=4y²x and v=3x²y, so, the right side becomes:

= ∫∫_R [∂(3x²y)/∂x - ∂(4xy²)/∂y] dx dy

= ∫∫_R (6xy - 8xy) dx dy

= -2 ∫ ∫ xy dx dy [from x=0 to 2 and y=0 to 2]

= -2 ∫ (∫ x dx) y dy

= -2 ∫ (2²/2 - 0²/2) y dy

= -4 ∫ y dy

= -8

Still have questions? Get your answers by asking now.