Question

3. Let F denote the vector field F(x, y, z) = <y, -x, y>. Evaluate the line integral integral_C F . dr where the closed curve C is the intersection of the elliptic paraboloid z = x^2 + y^2 with the plane z - 2x = 3, oriented counter-clockwise as viewed from the positive z-axis. (Hint: Use Stokes' Theorem)

          3. Let F denote the vector field
F(x, y, z) = <y, -x, y>.
Evaluate the line integral
integral_C F . dr
where the closed curve C is the intersection of the elliptic paraboloid z = x^2 + y^2 with the plane z - 2x = 3, oriented counter-clockwise as viewed from the positive z-axis. (Hint: Use Stokes' Theorem)

3. Let F denote the vector field
F(x, y, z) = <y, -x, y>.
Evaluate the line integral
integralC F . dr
where the closed curve C is the intersection of the elliptic paraboloid z = x^2 + y^2 with the plane z - 2x = 3, oriented counter-clockwise as viewed from the positive z-axis. (Hint: Use Stokes' Theorem)

Added by Teresa A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/25/2023

Step 1

First, we need to find the curve C. The intersection of the elliptic paraboloid $z = x^2 + y^2$ and the plane $2x = 3$ is given by $z = (\frac{3}{2})^2 + y^2$. Show more…

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Let F denote the vector field F(x,y,z) = <y,-x,y> Evaluate the line integral integral F . dr where the closed curve C is the intersection of the elliptic paraboloid z = x^2 + y^2 with the plane z - 2x = 3, oriented counter-clockwise as viewed from the positive z-axis. (Hint: Use Stokes' Theorem)