Calculate the work done by the force F(x, y) = x3yi+ (x - y)j along the parabola y= x2 from (-2, 4) to (1, 1). (See figure below for definition). Hint: the answer is an integer and r(t) = ti + ti2j, -2 < t < 1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Calculate the work done by the force F(x, y) = x3yi+ (x - y)j along the parabola y= x2 from (-2, 4) to (1, 1). (See figure below for definition).

Hint: the answer is an integer and r(t) = ti + ti2j, -2 < t < 1

Knowing that the integral ofa vector field
along a curve is defined by:
Definition: Let F be a continuous vector field
defined on a smooth curve C given by the
vector function r(t), a < t < b. So, the line
integral of F along C is:
SeF dr = F(r(1)) · r'(1) dt = Sc F•T ds
%3D
%3D
2
3
2
-2
0 1 2
2.
Transcribed Image Text:Knowing that the integral ofa vector field along a curve is defined by: Definition: Let F be a continuous vector field defined on a smooth curve C given by the vector function r(t), a < t < b. So, the line integral of F along C is: SeF dr = F(r(1)) · r'(1) dt = Sc F•T ds %3D %3D 2 3 2 -2 0 1 2 2.
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