(a)
To use:
The midpoint rule for double integral with six squares to estimate the area of the given surface
Solution:
Explanation:
1) Concept:
Use the formula for surface area and midpoint rule to evaluate it.
2) Formula and rule:
i) The surface area is
ii) Midpoint rule:
Where
3) Given:
4) Calculation:
Consider the given surface,
Differentiate
Differentiate
The area of the surface is given by,
Substitute the values,
Simplify,
By using midpoint rule with
Area of each sub rectangle is
Therefore,
Substituting the values,
By using calculator,
Conclusion:
The area of the given surface is
(b)
To use:
A computer algebra system to approximate the surface area in part (a) to four decimal places and compare it to the answer in part (a)
Solution:
Explanation:
1) Concept:
Use computer algebra system to evaluate the surface area and compare it to the answer in part (a).
2) Given:
3) Calculation:
From the part (a),
By using Mathematica,
Input:
Output:
Therefore, the surface area to four decimal places is
By comparing it with answer to part (a), it is correct up to first decimal place.
Conclusion:
Want to see the full answer?
Check out a sample textbook solutionChapter 16 Solutions
Calculus (MindTap Course List)
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