Question

Consider the vector field $\vec{F}$ and the curve C below. $\vec{F}(x, y) = (7 + 4xy^2)\vec{i} + 4x^2y\vec{j}$, C is the arc of the hyperbola $y = 1/x$ from $(1, 1)$ to $(3, \frac{1}{3})$ (a) Find a potential function $f$ such that $\vec{F} = \nabla f$. $f(x, y) = $ (b) Use part (a) to evaluate $\int_C \nabla f \cdot d\vec{r}$ along the given curve C.

Name: consider the vector field vecf and the curve c below vecfx y 7 4xy2veci 4x2yvecj c is the arc of the hyperbola y 1x from 1 1 to 3 frac13 a find a potential function f such that vecf nabla f 41633
Uploaded: 2022-06-07T08:47:34-08:00
Duration: 6 min 31 s
Channel: Shaiju T
Description: consider the vector field vecf and the curve c below vecfx y 7 4xy2veci 4x2yvecj c is the arc of the hyperbola y 1x from 1 1 to 3 frac13 a find a potential function f such that vecf nabla f 41633

          Consider the vector field $\vec{F}$ and the curve C below.
$\vec{F}(x, y) = (7 + 4xy^2)\vec{i} + 4x^2y\vec{j}$,
C is the arc of the hyperbola $y = 1/x$ from $(1, 1)$ to $(3, \frac{1}{3})$

(a) Find a potential function $f$ such that $\vec{F} = \nabla f$.
$f(x, y) = $

(b) Use part (a) to evaluate $\int_C \nabla f \cdot d\vec{r}$ along the given curve C.

$consider the vector field vecf and the curve c below vecfx y 7 4xy2veci 4x2yvecj c is the arc of the hyperbola y 1x from 1 1 to 3 frac13 a find a potential function f such that vecf nabla f 41633$

Added by Juan Luis S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

06/07/2022

Step 1

Given $\vec{F}(x, y) = (7 + 4xy^2)\vec{i} + 4x^2y\vec{j}$. If $\vec{F} = \nabla f$, then $\frac{\partial f}{\partial x} = 7 + 4xy^2$ and $\frac{\partial f}{\partial y} = 4x^2y$. Integrate $\frac{\partial f}{\partial x}$ with respect to $x$: $f(x, y) = \int (7 + Show more…

Show all steps

Thanks for your feedback!

Consider the vector field $\vec{F}$ and the curve C below. $\vec{F}(x, y) = (7 + 4xy^2)\vec{i} + 4x^2y\vec{j}$, C is the arc of the hyperbola $y = 1/x$ from $(1, 1)$ to $(3, \frac{1}{3})$ (a) Find a potential function $f$ such that $\vec{F} = \nabla f$. $f(x, y) = $ (b) Use part (a) to evaluate $\int_C \nabla f \cdot d\vec{r}$ along the given curve C.