Question

Determine the potential for the field: \(\vec{F} = (6x^2y + 4y^2 + 3y, 2x^3 + 8xy + 3x + 2)\) Do not put the constant \("+c"\) for the potential in your answer below. f(x, y) = 2x^3y + 4xy^2 + 3xy Now calculate \(\int_C \vec{F} \cdot d\vec{r}\) where C is the path of the parabola y = x^2 - 2x - 13 from the point (0, -13) to the point (-3, 2) The line integral equals -174

          Determine the potential for the field:
\(\vec{F} = (6x^2y + 4y^2 + 3y, 2x^3 + 8xy + 3x + 2)\)
Do not put the constant \("+c"\) for the potential in your answer below.
f(x, y) = 2x^3y + 4xy^2 + 3xy
Now calculate
\(\int_C \vec{F} \cdot d\vec{r}\)
where C is the path of the parabola y = x^2 - 2x - 13 from the point (0, -13) to the point (-3, 2)
The line integral equals -174

Determine the potential for the field:
F⃗ = (6x^2y + 4y^2 + 3y, 2x^3 + 8xy + 3x + 2)
Do not put the constant "+c" for the potential in your answer below.
f(x, y) = 2x^3y + 4xy^2 + 3xy
Now calculate
F⃗· dr⃗
where C is the path of the parabola y = x^2 - 2x - 13 from the point (0, -13) to the point (-3, 2)
The line integral equals -174

Added by Emily S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/04/2023

Step 1

In other words, we need to find a function φ(x, y) such that: ∂φ/∂x = 6xy + 3y^2x^3 + 8y + 3x ∂φ/∂y = 4y + 6xy + 3x^3y^2 Show more…

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Determine the potential for the field F = 6xy + 4y + 3y^2x^3 + 8xy + 3x + 2. Do not put the constant "+c" for the potential in your answer below. fy = 2x^3y + 4x*y^2 + 3xy Tries 1/8 Now calculate where C is the path of the parabola y = 2 - 13 from the point 0, -13 to the point -3, 2. The line integral equals -174.