Given the vector A = (x2 − y2)i + 2xyj.(a) Find ∇ × A.(b) Evaluate RR (∇ × A) · dσ over a rectangle in the (x, y) plane bounded by the lines x = 0, x = a, y = 0, y = b.(c) Evaluate H A· dr around the boundary of the rectangle and thus verify Stokes’ theorem for this case. Use either Stokes’ theorem or the divergence theorem to evaluate each of the following integrals in the easiest possible way.
Given the vector A = (x2 − y2)i + 2xyj.(a) Find ∇ × A.(b) Evaluate RR (∇ × A) · dσ over a rectangle in the (x, y) plane bounded by the lines x = 0, x = a, y = 0, y = b.(c) Evaluate H A· dr around the boundary of the rectangle and thus verify Stokes’ theorem for this case. Use either Stokes’ theorem or the divergence theorem to evaluate each of the following integrals in the easiest possible way.
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Given the vector A = (x2 − y2)i + 2xyj.
(a) Find ∇ × A.
(b) Evaluate RR (∇ × A) · dσ over a rectangle in the (x, y) plane bounded by the lines x = 0, x = a, y = 0, y = b.
(c) Evaluate H A· dr around the boundary of the rectangle and thus verify Stokes’ theorem for this case.
Use either Stokes’ theorem or the divergence theorem to evaluate each of the following integrals in the easiest possible way.
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