Chapter 12: Q56E (page 709)
\({\rm{D}}\)is the disk with centre the origin and radius \({\rm{R}}\).
xy
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Set up, but do not evaluate, integral expressions for
The hemisphere .\({{\text{x}}^{\text{2}}}\text{+}{{\text{y}}^{\text{2}}}\text{+}{{\text{z}}^{\text{2}}}\text{1,z}\approx \text{0; }\!\!\rho\!\!\text{ (x,y,z)=}\sqrt{{{\text{x}}^{\text{2}}}\text{+}{{\text{y}}^{\text{2}}}\text{+}{{\text{z}}^{\text{2}}}}\).
Find the mass and center of mass of the solid with the given density function \({\rm{q}}\).
\({\rm{E}}\) is the tetrahedron bounded by the planes \({\rm{x = 0,y = 0,}}\)\({\rm{z = 0, x + y = 1; q(x,y,z) = y}}\)
Calculate the double integral
\(\int {\int\limits_r {x\sin \left( {x + y} \right)dA,R = \left( {0,\frac{\pi }{6}} \right)X\left( {0,\frac{\pi }{3}} \right)} } \)
Express D as a region of Type 1. And also as a region of type 2. Then evaluate the double integral in 2 ways.
D is enclosed by the lines \(y = x,y = 0,x = 1\)
Evaluate the iterated integral \(\int_0^2 {\int_y^{2y} x } ydxdy\)
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