?Verify that Green's Theorem is true for the line integral \(\int_C x y^2 d x-x^2 y d

Chapter 16, Problem 15

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QUESTION:

Verify that Green's Theorem is true for the line integral \(\int_C x y^2 d x-x^2 y d y\), where C consists of the parabola \(y=x^2\) from (-1, 1) to (1, 1) and the line segment from (1, 1) to (-1, 1)

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QUESTION:

Verify that Green's Theorem is true for the line integral \(\int_C x y^2 d x-x^2 y d y\), where C consists of the parabola \(y=x^2\) from (-1, 1) to (1, 1) and the line segment from (1, 1) to (-1, 1)

ANSWER:

Step 1 of 6

Green’s Theorem states that,

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