Concept explainers
(a)
To find:
Solution:
Explanation:
1) Concept:
If
2) Given:
3) Calculation:
If
Integrate
Notice that the constant of integration is a constant with respect to
Now differentiate above equation with respect to
Comparing (2), and (4)
Integrating with respect to
Hence (4) becomes
Differentiate with respect to
Comparing this equation with (1)
Integrate with respect to
Therefore, (6) becomes,
Conclusion:
(b)
To evaluate:
Solution:
Explanation:
1) Concept:
Fundamental theorem of line integral:
Let
2) Given:
3) Calculation:
C is a smooth curve with initial point
So, by using concept,
Since
Therefore,
Therefore,
From the answer of part (a),
Therefore,
Conclusion:
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Calculus (MindTap Course List)
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