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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
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 1st 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 \(S\).