Let S be the closed surface consisting of the cylinder. C. C= {(x, y, z): x^2+y^2 = 4.0 le z le 3 together with the bottom, b = {(x,y,0): x^2+y^2 le 4} and the top. T= {(x,y,3):x^2+y^2 le 4} Let F(x, y, z)=(3z^2 x+10x^3)i+(z^3 yx + y)j + sin (z^4 x^2)k Find (times F+ 2zk) "dot" dS assuming that S is oriented with the outward-pointing normal
Show transcribed image text Let S be the closed surface consisting of the cylinder. C. C= {(x, y, z): x^2+y^2 = 4.0 le z le 3 together with the bottom, b = {(x,y,0): x^2+y^2 le 4} and the top. T= {(x,y,3):x^2+y^2 le 4} Let F(x, y, z)=(3z^2 x+10x^3)i+(z^3 yx + y)j + sin (z^4 x^2)k Find (times F+ 2zk) "dot" dS assuming that S is oriented with the outward-pointing normal