To find: The volume of the solid generated by resolving the region bounded by the curves.
Answer to Problem 40E
The volume of the solid generated is
Explanation of Solution
Given information:
Calculation:
Let's graph this area in Desmos and draw some conclusions based on it.
From the graph, the region is bounded by the curve
Let’s consider the cases
Considering the case
Considering the case
The limits of integration
Finding the formulas for
Thus, the volume of the solid is the sum of these integrals.
To find the formula for
Since each cross section on height
The area of cross section is given by,
To find the formula for
Since each cross section on height
The area of cross section is given by,
Finding the values of
The volume of the solid is given by,
Therefore, the volume of the solid generated is
Chapter 7 Solutions
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