Chapter 12: Q4E (page 707)
Evaluate the iterated integral \(\int_0^2 {\int_y^{2y} x } ydxdy\)
Value of integral is \(6\).\(\)
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To sketch the solid whose volume is given by the iterated integral and evaluate it.
Find the volume of the solid lying under the elliptic paraboloid \(\frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} + z = 1\) and above the rectangle \(R = \left( { - 1,1} \right)X\left( { - 2,2} \right)\)
Find the volume of the solid that lies under the plane \(4x + 6y - 2z + 15 = 0\) and above the triangle
\(R = \left\{ {\left( {x,y} \right)| - 1 \le x \le 2, - 1 \le y \le 1} \right\}\)
find the volume of the solid that lies under the hyperbolic paraboloid \(z = 3{y^2} - {x^2} + 2\) and above the rectangle \(R = \left( { - 1,1} \right)X\left( {1,2} \right)\)
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 \({\rm{x = 0,y = 0,}}\)\({\rm{z = 0, x + y = 1; q(x,y,z) = y}}\)
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