Calculus III - Surface Integrals (Assignment Problems)

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Section 17.3 : Surface Integrals

Evaluate $\displaystyle \iint\limits_{S}{{2x - 3y + z\,dS}}$ where $S$ is the portion of $x + y + z = 2$ that is in the 1^st octant.
Evaluate $\displaystyle \iint\limits_{S}{{x + {y^2} + {z^2}\,dS}}$ where $S$ is the portion of $x = 4 - {y^2} - {z^2}$ that lies in front of $x = - 2$ .
Evaluate $\displaystyle \iint\limits_{S}{{6\,dS}}$ where $S$ is the portion of $y = 4z + {x^3} + 6$ that lies over the region in the xz-plane with bounded by $z = {x^3}$ , $x = 1$ and the $x$ -axis.
Evaluate $\displaystyle \iint\limits_{S}{{xyz\,dS}}$ where $S$ is the portion of ${x^2} + {y^2} = 36$ between $z = - 3$ and $z = 1$ .
Evaluate $\displaystyle \iint\limits_{S}{{{z^2} + x\,dS}}$ where $S$ is the portion of ${x^2} + {y^2} + {z^2} = 4$ with $z \ge 0$ .
Evaluate $\displaystyle \iint\limits_{S}{{4y\,dS}}$ where $S$ is the portion of ${x^2} + {z^2} = 9$ between $y = 2$ and $y = 10 - x$ .
Evaluate $\displaystyle \iint\limits_{S}{{z + 3\,dS}}$ where $S$ is the surface of the solid bounded by $z = 2{x^2} + 2{y^2} - 3$ and $z = 1$ . Note that both surfaces of this solid are included in $S$ .
Evaluate $\displaystyle \iint\limits_{S}{{z\,dS}}$ where $S$ is the surface of the solid bounded by ${y^2} + {z^2} = 4$ , $x = y - 3$ , and $x = 6 - z$ . Note that all three surfaces of this solid are included in $S$ .
Evaluate $\displaystyle \iint\limits_{S}{{4 + z\,dS}}$ where $S$ is the portion of the sphere of radius 1 with $z \ge 0$ and $x \le 0$ . Note that all three surfaces of this solid are included in $S$ .