Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z ≥ 0. (a) Suppose that S is parameterized by r(θ, y) = (3 cos(θ), y, 3 sin(θ)) whit θ in [0,π/2]; and y  in [0, 2] , Use this parametrization to find the area of ​​´ S. (b) Justify that ~ n = (x = 3,0; z = 3) is a vector normal to S, and use it to find the value of the surface integral  ∫ ∫ FndS, where F(x; y; z) = (3x,y^5,3z).

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.