Verify Stokes’ Theorem if the surface S is the portion of the paraboloid z = 4...

Question

Question

Verify Stokes’ Theorem if the surface S is the portion of the paraboloid z = 4 − x2 − y2 for which z ≥ 0 and F(x,y,z) = 2zi+3xj +5yk.

math calculus

Answer 1

Answer #1

stokes theorem ff curlF nds = [F.dr [Fdr : C is parametrized as follows z=0.z=4-x2 - y2 4=x2 + y2 x=2cost.y=2 sint.z=0 F.dr=2

curlF = lax û az 22 3x5y| =i(5)-;(-2)+k(3) =5i+2j+3k n=(2x, 2 y.1) curlF nds = (10x + 4y + 3) dxdy by using poalr cordinaets

Answer 2

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