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# Tutorial ExercisoEvaluate the surface integralfor the given vector field and the oriented surface 5_ In otherwords; find the flux of F across 5_ For closed surfaces...

## Question

###### Tutorial ExercisoEvaluate the surface integralfor the given vector field and the oriented surface 5_ In otherwords; find the flux of F across 5_ For closed surfaces, use the positive (outward) orientation;F(x, Y, 2) = xy | + yz j + zx k 5 is the part of the paraboloid 2 = 3 ~ x2 _ y2 that lies above the square 0 $x$ 1, 0 $Y$ 1, and has upward orientationStepSince 5 is part of the paraboloid 2 = g(x, Y) = 3 - x _y, it is the graph of function, and SO we know that f ds = Fls (~pBk Thus, we ha

Tutorial Exerciso Evaluate the surface integral for the given vector field and the oriented surface 5_ In other words; find the flux of F across 5_ For closed surfaces, use the positive (outward) orientation; F(x, Y, 2) = xy | + yz j + zx k 5 is the part of the paraboloid 2 = 3 ~ x2 _ y2 that lies above the square 0 $x$ 1, 0 $Y$ 1, and has upward orientation Step Since 5 is part of the paraboloid 2 = g(x, Y) = 3 - x _y, it is the graph of function, and SO we know that f ds = Fls (~pBk Thus, we have the following. fI ds J ' J ' [~xt-zx) - yz( - 2y) + Zx Jo' J " [zxky_ 2y2(3 - x2 _ v2) + x(3 _ x2 _ y2)] dA Jo ' Jo " (2xy+[6y2 2x2y2 _ 2y4 + 3x - x3 6y- 2912 2y'+30 - r dy dx Step 2 Now, we have the following (Zx2y 6y2 Zx2y2 _ 2y4 + 3x x xy2) dy 3x Suhmit Skip (you cannot come back)