(a) Find a function f such that F = ∇ f and (b) use part (a) to evaluate ∫C F · dr along the given curve C.
15. F(x, y, z) = yz i + xz j + (xy + 2z) k,
C is the line segment from (1, 0, −2) to (4, 6, 3)
To find: The potential function f such that .
Vector field is .
Write the relation between the potential function f and vector field .
Substitute for ,
Compare the equation with .
Integrate equation (1) with respect to x.
Apply partial differentiation with respect to y on both sides of equation (4).
Compare the equations (2) and (5)
The value of along the curve C.
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Calculus: Early Transcendental Functions
Finite Mathematics and Applied Calculus (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: An Applied Approach (MindTap Course List)
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Essentials Of Statistics
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Single Variable Calculus
Probability and Statistics for Engineering and the Sciences
Understanding Basic Statistics
Contemporary Mathematics for Business & Consumers
Mathematical Applications for the Management, Life, and Social Sciences
Mathematical Excursions (MindTap Course List)
Elementary Technical Mathematics
Elementary Geometry For College Students, 7e
Single Variable Calculus: Early Transcendentals
Calculus: Early Transcendental Functions (MindTap Course List)
Calculus of a Single Variable
Trigonometry (MindTap Course List)
Elements Of Modern Algebra
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Multivariable Calculus, 8th
Finite Mathematics for the Managerial, Life, and Social Sciences
Elementary Geometry for College Students