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Chapter 14: Q. 48 (page 1120)
Find the integral of on the portion of the plane with the equation
with 2 鈮� x 鈮� 7 and 1 鈮� z 鈮� 2.
Ans:
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, where S is the portion of the plane with equation that lies on the positive side of the rectangle with cornersin theyz-plane.
Area: Finding the area of a region in the x y-plane is one of the motivating applications of integration. It is also a special case of the surface area calculation developed in this section. Find the area of the region in the x y-plane bounded by the curves
Use what you know about average value from previous sections to propose a formula for the average value of a multivariate function f(x, y, z) on a smooth surface S.
If the velocity of a flow of a gas at a point (x, y, z) is represented by F and the gas is expanding at that point, what does this imply about the divergence of F at the point?
Work as an integral of force and distance: Find the work done in moving an object along the x-axis from the origin to if the force acting on the object at a given value of x is role="math" localid="1650297715748" .
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