Question

Calculate the value of the line integral $I = \int \frac{x \, dy - y \, dx}{x^2 + y^2}$, along the two paths from $(-1, 0)$ to $(1, 0)$ shown in the figure at right. You should find that for both paths $I = \pi$.

          Calculate the value of the line integral
$I = \int \frac{x \, dy - y \, dx}{x^2 + y^2}$,
along the two paths from $(-1, 0)$ to $(1, 0)$ shown in the
figure at right. You should find that for both paths
$I = \pi$.

Calculate the value of the line integral
I = ∫(x dy - y dx)/(x^2 + y^2),
along the two paths from (-1, 0) to (1, 0) shown in the
figure at right. You should find that for both paths
I = π.

Added by Edwin W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Animesh Raj

Step 1

For the first path, we can use the parameterization x = t and y = 0, where t ranges from -1 to 1. For the second path, we can use the parameterization x = cos(t) and y = sin(t), where t ranges from 0 to π. Now, let's calculate the line integral for each Show more…

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Calculate the value of the line integral xdy - ydx over x^2 + y^2 (5) along the two paths from (-1,0) to (1,0) shown in the figure at right. You should find that for both paths, I = (-1.0, 0.1, 1.0).