The give integral is
where C is the boundary of the region in first quadrant bounded by
From greens theorem we know that
Comparing we get
From (1), (2) and (3) we get
Now, we will find the region of integration.
Since the region lies on first quadrant so we leave negative sign.
Therefore, x varies from 0 to 2 and y varies from 4 to x2
Now, from (4)
Find the region that one of the cycloid's arcs borders ,where a > 0, and , and the axis(use Green's theorem).
Using the two approaches below, evaluate the line integral. y) dx + (x+y)dy C os counerclockwise around the circle with center the origin and radius 3(a) directly (b) using Green's Theorem.
Use the Divergence Theorem to calculate the surface integral F · dS, that is, calculate the flux of F across S.
S is the surface of the solid bounded by the cylinder