Purchase Solution

Vector field line integral

Not what you're looking for?

Ask Custom Question

Consider the vector field F = (x^2 - y^2)i + (y^2 - Z^2)j + (z^2 - x^2)k.

a) Calculate the line integral of F from P_0 at (1,0,0) to P_1 at (-1,0,0) along the direct line path joining these points.
B) Calculate the line integral of F from P_0 at (1,0,0) to P_1 at (-1,0,0) along the horizontal semicircular path joining these points, traversed anti-clockwise (through the point (0,1,0)), which forms part of the circle centred at the origin. You may need to use sin^3t = sint(1-cos^2t).

Purchase this Solution
Solution Summary

This solution considers the vector field, and calculates line integrals.

Solution Preview

Hello and thank you for posting your question to Brainmass.
The solution is attached below in ...

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Gradient Vector Fields and Line Integrals

    The line integral of a vector field on a curve is defined by (1) For the line integral c1 The line integral is (2) line integral c2 The line integral is The force is not a gradient vector field.

  • Relates Line Integral to the Polar Moment of Inertia (PMOI)

    26705 Prove that the Line Integral of a Vector Field along a Contour C is equal to the Polar Moment of Inertia of the region R lying below C and above the x-axis.

  • divergence and curl of the given vector field

    327040 divergence and curl of the given vector field Calculate the divergence and curl of the given vector field F.

  • Vector Fields, Fundamental Theorem of Line Integrals

    118615 Vector Fields, Fundamental Theorem of Line Integrals 1. Find the curl of the vector field F at the indicated point: 2. Evaluate the following line integral using the Fundamental theorem of line Integrals: 3.

  • Gradient Functions

    Since the curl of the vector field F is 0. then the line integral is independent of the path. Now for any point (x1, y1, z1) in the space, we choose direct line from the origin (0, 0, 0) to this point as the path.

  • Integrals

    So, let's get the vector field evaluated along the curve: Now we need the derivate of the parameterization: The dot product is then The line integral is Its derivative is The vector field evaluated along the curve: The dot

  • Vector fields

    29257 Vector Fields for Evaluating Integrals Let a vector field F be given by F(x,y,z) = (x^3)i - (y^2)j + (2yz)k and a curve C be given by r(t) = 2ti + sintj - costk, 0 <= t <= (pi/2) 1. Evaluate the line integral F*dr. 2.

  • Vector Integrals : Stokes' Theorem and Line Integral of a Vector Field

    The line integral of a vector field is calculated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

  • Vector field

    This solution provides a vector field and shows that it is the gradient of a given polar angle function, then gives characteristics of a smooth curve and shows how to express the integral in polar coordinates.

View More Related Solutions