Use Greens Theorem to find the counterclockwise circulation and the outward flux

Question

Use Greens Theorem to find the counterclockwise circulation and the outward flux of field F = (y2 - x2)i + (y2 + x2)j and the curve C: The triangle bounded by y=0, x=3, and y=x. Use Green's Theorem to evaluate the integral 3ydy + 2xdy where C is the boundary of 0 x pi, 0 y sinx. Find the surface area of the cap cut from the sphere x2 + y2 + z2 = 2 and by the cone z = Find the flux of the Field F = xi + yj + zk across the position of the sphere x2 + y2 + z2 = a2 in the first octant in the direction away from the origin.

Explanation / Answer

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