EXPLORING CONCEPTS Using Different Methods Evaluate ∫ S ∫ ( x + 2 y ) d S where S is the first-octant portion of the plane 2 x + 2 y + z = 4 by projecting 5 onto (a) the xy -plane, (b) the xz -plane, and (c) the yz -plane. Verify that all answers are the same.
EXPLORING CONCEPTS Using Different Methods Evaluate ∫ S ∫ ( x + 2 y ) d S where S is the first-octant portion of the plane 2 x + 2 y + z = 4 by projecting 5 onto (a) the xy -plane, (b) the xz -plane, and (c) the yz -plane. Verify that all answers are the same.
Solution Summary: The author calculates the value of integral by projecting S onto the xy -plane where S is the first-octant portion of the plane.
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