Chapter 12: Q2E (page 728)
To evaluate the integral of by arranging different orders of integration.
The value of the given integral is \(21\)
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Find the moment of inertia about the z -axis of the solid.
Find the volume of the solid that lies under the plane \(4x + 6y - 2z + 15 = 0\) and above the triangle
\(R = \left\{ {\left( {x,y} \right)| - 1 \le x \le 2, - 1 \le y \le 1} \right\}\)
Evaluate\(\iiint_{\text{E}}{\text{z}}\text{dV}\), where \({\rm{E}}\) is enclosed by the paraboloid \({\rm{z = }}{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}\) and the plane \({\rm{z = 4}}\). Use cylindrical coordinates.
Set up, but do not evaluate, integral expressions for
The hemisphere .\({{\text{x}}^{\text{2}}}\text{+}{{\text{y}}^{\text{2}}}\text{+}{{\text{z}}^{\text{2}}}\text{1,z}\approx \text{0; }\!\!\rho\!\!\text{ (x,y,z)=}\sqrt{{{\text{x}}^{\text{2}}}\text{+}{{\text{y}}^{\text{2}}}\text{+}{{\text{z}}^{\text{2}}}}\).
Evaluate \(\iiint_{\text{E}}{\text{(x+y+z)}}\text{dV}\) , where \({\rm{E}}\) is the solid in the first octant that lies under the paraboloid \({\rm{z = 4 - }}{{\rm{x}}^{\rm{2}}}{\rm{ - }}{{\rm{y}}^{\rm{2}}}\). Use cylindrical coordinates.
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