A particle moves along the curve R = (2t³ + 4t²) i + (3t² - 5t) j + (7t² + 6t) k, where t is the time. The velocity component of the particle in the direction 3...

Let the vector v = vi + vj + vak be a differentiable vector function of Cartesian coordinates x, y and z. The curl of the vector v is given by curl v =

For vectors F = 3xy î − y² ĵ and R = x î + y ĵ, the value of ∮C F.dR on the curve C (y = 2x²) in the x-y plane from (0, 0) to (1, 2) is