Consider out counterclockwise. fo x²y dx - xy² dy, where C is the boundary of the region 0 ≤ y ≤ √√4 - x², traced Compute the line integral(s) directly. Use Green's Theorem to compute the line integral. Is F conservative? Answer this question in two ways: fields, and (ii) use your results in parts (a) and (b). use the test for conservative vector

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.5: The Area Between Two Curves
Problem 21E
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Consider
out counterclockwise.
fa²y dx - xy² dy, where O' is the boundary of the region 0 ≤ y ≤ √4 - x², traced
Compute the line integral(s) directly.
Use Green's Theorem to compute the line integral.
Is F conservative? Answer this question in two ways: (i) use the test for conservative vector
fields, and (ii) use your results in parts (a) and (b).
Transcribed Image Text:Consider out counterclockwise. fa²y dx - xy² dy, where O' is the boundary of the region 0 ≤ y ≤ √4 - x², traced Compute the line integral(s) directly. Use Green's Theorem to compute the line integral. Is F conservative? Answer this question in two ways: (i) use the test for conservative vector fields, and (ii) use your results in parts (a) and (b).
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