Can someone show me step by step how to work this problem out please.
Let C be the triangle with vertices (0,0), (1,0), and (1,2). Find the following line integral by two methods, directly and using greens theorem.
2xy^2dx + yx^2dy
Thanks!!!
Can someone show me step by step how to work this problem out please.
Let C be the triangle with vertices (0,0), (1,0), and (1,2). Find the following line integral by two methods, directly and using greens theorem.
2xy^2dx + yx^2dy
Thanks!!!
Per Green's Theorem:
The equation of the line from (0,0) to (1,2) is y=2x.
$\displaystyle f(x,y)=2xy^{2}, \;\ g(x,y)=x^{2}y$
$\displaystyle \int_{C}2xy^{2}dx+x^{2}ydy=\int\int\left[\frac{\partial}{\partial{x}}(x^{2}y)-\frac{\partial}{\partial{y}}(2xy^{2})\right]dA=\int_{0}^{1}\int_{0}^{2x}(-2xy)dydx$
Can you finish up?.