Question

1. Under the surface z = x³y? + xy² and above the region bounded by the curves y = x³ - x and y = x² + x for x ? 0 2. Find the volume of the solid under the plane 3x + 2y - z = 0 and above the region enclosed by the parabolas y = x² and x = y² 3. Find the volume of the solid S that is bounded by the elliptic paraboloid x² + 2y² + z = 16, the planes x = 2 and y = 2, and the three coordinate planes. 4. Find the volume of the solid lying under the plane z = 2x + 5y + 1 and above the rectangle R = {(x, y)| -1 ? x ? 0, 1 ? y ? 4} 5. Find the volume of the tetrahedron bounded by the planes x + 2y + z = 2, x = 2y, x = 0 and z = 0. Sketch the diagram of the tetrahedron with labeled points with coordinate axes and the boundary equations. 6. Evaluate (iint_D xy , dA), where D is the region bounded by the line y = x - 1 and the parabola y² = 2x + 6. Sketch a diagram of the region showing equations of the boundaries and the coordinates of the end points. 7. Evaluate the region of integration given by $int_0^{pi/4} int_0^{cos y} x^2 sin y , dx , dy$ 8. Find the volume of the region in space, the region beneath z = 4x² + 9y² and above the rectangle with vertices (0,0), (3,0), (3,2), (0,2) in the xy- plane. Sketch it.

          1. Under the surface z = x³y? + xy² and above the region bounded by the curves y = x³ - x and
y = x² + x for x ? 0
2. Find the volume of the solid under the plane 3x + 2y - z = 0 and above the region enclosed by the
parabolas y = x² and x = y²
3. Find the volume of the solid S that is bounded by the elliptic paraboloid x² + 2y² + z = 16, the
planes x = 2 and y = 2, and the three coordinate planes.
4. Find the volume of the solid lying under the plane z = 2x + 5y + 1 and above the rectangle R =
{(x, y)| -1 ? x ? 0, 1 ? y ? 4}
5. Find the volume of the tetrahedron bounded by the planes
x + 2y + z = 2, x = 2y, x = 0 and z = 0. Sketch the diagram of the tetrahedron with
labeled points with coordinate axes and the boundary equations.
6. Evaluate (iint_D xy , dA), where D is the region bounded by the line y = x - 1 and the parabola
y² = 2x + 6. Sketch a diagram of the region showing equations of the boundaries and the
coordinates of the end points.
7. Evaluate the region of integration given by
$int_0^{pi/4} int_0^{cos y} x^2 sin y , dx , dy$
8. Find the volume of the region in space, the region beneath z = 4x² + 9y² and above the rectangle
with vertices (0,0), (3,0), (3,2), (0,2) in the xy- plane. Sketch it.

1. Under the surface z = x³y? + xy² and above the region bounded by the curves y = x³ - x and
y = x² + x for x ? 0
2. Find the volume of the solid under the plane 3x + 2y - z = 0 and above the region enclosed by the
parabolas y = x² and x = y²
3. Find the volume of the solid S that is bounded by the elliptic paraboloid x² + 2y² + z = 16, the
planes x = 2 and y = 2, and the three coordinate planes.
4. Find the volume of the solid lying under the plane z = 2x + 5y + 1 and above the rectangle R =
(x, y)| -1 ? x ? 0, 1 ? y ? 4
5. Find the volume of the tetrahedron bounded by the planes
x + 2y + z = 2, x = 2y, x = 0 and z = 0. Sketch the diagram of the tetrahedron with
labeled points with coordinate axes and the boundary equations.
6. Evaluate (iintD xy , dA), where D is the region bounded by the line y = x - 1 and the parabola
y² = 2x + 6. Sketch a diagram of the region showing equations of the boundaries and the
coordinates of the end points.
7. Evaluate the region of integration given by
int0^pi/4 int0^cos y x^2 sin y , dx , dy
8. Find the volume of the region in space, the region beneath z = 4x² + 9y² and above the rectangle
with vertices (0,0), (3,0), (3,2), (0,2) in the xy- plane. Sketch it.

Added by Lori N.

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