8. Let S be the part of cylinder y2 + z2 = 4 that lies above the rectangle with vertices (0,0), (1,0), (1,2) and (0,2). Find the area of the surface S. __(h)__

2. (10 分) Let C be a positively oriented, piecewise-smooth, simple closed curve in the plane and let D be the region bounded by C. If f(x, y) is a scalar function with continuous first and second partial derivatives in D, derive the following formula: ∬D ( fxx + fyy )dxdy =where = ∇f⋅N is the normal derivative, N is an outer unit normal, s is the arc-length.

8. Let S be the part of cylinder y² + z² = 4 that lies above the rectangle with vertices (0,0), (1,0), (1,2) and (0,2). Find the area of the surface S. (h)

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