(a)
To show:
Solution:
Explanation:
1) Concept:
Compare
2) Given:
3) Calculations:
Let
Comparing
Differentiating
By using the quotient rule of differentiation,
Differentiating
From
Conclusion:
(b)
To show:
Solution:
i) The integral
ii) This does not contradict theorem 6.
Explanation:
1) Concept:
Let
2) Given:
3) Calculation:
i)
By using the given hint,
Let
The parametric equation for
Let
The parametric equation for
Substitute
Differentiating
By using the concept,
By integrating,
By using the fundamental theorem of calculus,
Also, by using the concept,
By integrating,
By using the fundamental theorem of calculus,
Since,
ii)
The domain of
That is,
The domain of
This doesn’t contradict theorem 6, since the domain of
Conclusion:
i) The integral
ii) This does not contradict theorem 6.
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