Finding the Volume of a Solid Region In Exercises 1-6, find the volume of the solid region bounded in the first octant by the plane. See Example 1.
To calculate: The volume of solid region bounded in first octane and the plane
Given information:
The provided equation of plane is
Formula used:
The procedure to calculate volume of surface
Step-1: Write the equation of surface in the form
Step-2: Sketch the projected region R in the x-y-plane.
Step-3: Determine the order of limits of integration.
Step-4: Evaluate the volume of solid region,
Here, the projected region is R:
Calculation:
Consider equation of plane,
The following table shown different coordinate of
y-Coordinate | z-Coordinate | ||
The graph of function
Substitute, 0 for z in equation of plane
The following table shown different coordinate of
y-Coordinate | ||
The graph of equation
One way to set up the double integration is to choose x as the outer variable with that choice. The bounds for x are
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