Question

Consider F and C below. $F(x, y) = (8 + 8xy^2)i + 8x^2yj$, C is the arc of the hyperbola $y = \frac{1}{x}$ from $(1, 1)$ to $(5, \frac{1}{5})$ (a) Find a function $f$ such that $F = \nabla f$. $f(x, y) = \text{________}$ (b) Use part (a) to evaluate $\int_C F \cdot dr$ along the given curve C.

Name: consider f and c below fx y 8 8xy2i 8x2yj c is the arc of the hyperbola y frac1x from 1 1 to 5 frac15 a find a function f such that f nabla f fx y text b use part a to evaluate intc 83443
Uploaded: 2022-12-09T06:35:07-08:00
Duration: 5 min 7 s
Channel: Madhur L
Description: consider f and c below fx y 8 8xy2i 8x2yj c is the arc of the hyperbola y frac1x from 1 1 to 5 frac15 a find a function f such that f nabla f fx y text b use part a to evaluate intc 83443

          Consider F and C below.
$F(x, y) = (8 + 8xy^2)i + 8x^2yj$, C is the arc of the hyperbola $y = \frac{1}{x}$ from $(1, 1)$ to $(5, \frac{1}{5})$
(a) Find a function $f$ such that $F = \nabla f$.
$f(x, y) = \text{________}$
(b) Use part (a) to evaluate $\int_C F \cdot dr$ along the given curve C.

$consider f and c below fx y 8 8xy2i 8x2yj c is the arc of the hyperbola y frac1x from 1 1 to 5 frac15 a find a function f such that f nabla f fx y text b use part a to evaluate intc 83443$

Added by Erin W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

12/09/2022

Step 1

Integrating the first equation with respect to $x$, we get: $f(x, y) = \int (8 + 8xy^2) dx = 8x + 4x^2y^2 + g(y)$, where $g(y)$ is an arbitrary function of $y$. Now, we differentiate this expression with respect to $y$: $\frac{\partial f}{\partial y} = 8x^2y + Show more…

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Consider F and C below. $F(x, y) = (8 + 8xy^2)i + 8x^2yj$, C is the arc of the hyperbola $y = \frac{1}{x}$ from $(1, 1)$ to $(5, \frac{1}{5})$ (a) Find a function $f$ such that $F = \nabla f$. $f(x, y) = \text{________}$ (b) Use part (a) to evaluate $\int_C F \cdot dr$ along the given curve C.