Changing orientation Let f(x, y) = x and let C be the

Chapter 13, Problem 55E

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QUESTION:

Changing orientation Let \(f(x, y)=x\) and let C be the segment of the parabola \(y=x^{2}\) joining O(0, 0) and P(1, 1).

a. Find the parameterization of C in the direction from O to P. Evaluate \(\int_{C} f d s\).

b. Find the parameterization of C in the direction from P to O. Evaluate \(\int_{C} f d s\).

c. Compare the results of (a) and (b).

Questions & Answers

QUESTION:

Changing orientation Let \(f(x, y)=x\) and let C be the segment of the parabola \(y=x^{2}\) joining O(0, 0) and P(1, 1).

a. Find the parameterization of C in the direction from O to P. Evaluate \(\int_{C} f d s\).

b. Find the parameterization of C in the direction from P to O. Evaluate \(\int_{C} f d s\).

c. Compare the results of (a) and (b).

ANSWER:

Solution 55E

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