
Concept explainers
(a)
To find area of region R
(a)

Answer to Problem 53RE
Area of Region R
Explanation of Solution
Given:
Region R in the first quadrant enclosed by the y-axis and the graphs of
Concept Used:
Area between the curves
Given region R is in the first quadrant by the y-axis and the graphs of
Getting limits by solving using graphing calculator
Therefore,
Limits are
Calculation:
Area of region R,
Conclusion:
Area of Region R
(b)
To find the volume of the solid generated when region R is revolved about
(b)

Answer to Problem 53RE
Volume of the solid generated when region R is revolved about
Explanation of Solution
Given:
Region R in the first quadrant enclosed by the y-axis and the graphs of
Concept Used:
The volume V of a solid generated by revolving the region about
Calculation:
Now finding definite integral,
Conclusion:
Required Volume, V=
c.
To find volume of the solid whose base is region R and whose cross sections cut by planes perpendicular to
c.

Answer to Problem 53RE
Volume of the solid whose base is region R and whose cross sections cut by planes perpendicular to
Explanation of Solution
Given:
The solid whose base is region R and whose cross sections cut by planes perpendicular to
Concept Used:
Volume of the solid whose base is region R and whose cross sections cut by planes perpendicular to
Calculation:
Now finding definite integral by putting values of limits
Conclusion:
Required Volume
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