Purchase Solution

Vectors Calculas & Applications

Not what you're looking for?

Ask Custom Question

See the attached file.

1. Evaluate the integral:
** see the attachment for the full equation **

Where D is the domain given by: 1 ≤ x^2 + y^2 ≤ 4 and y ≥ 0.

2. (i) Find the area of the region enclosed by the ellipse (x^2/a^2) + (y^2/b^2) = 1

(ii) Find the area of the region enclosed by the parabola y = x^2 and the line y= x + 2.
Sketch the region.

3. Calculate the mass of a spherical bead of radius 3, centered at the origin, if the density of the material it is made of, is given by the function :
p(x,y,z)=2|z|

4. Evaluate the moment of inertia of a cylinder of radius R and height L about its axis of symmetry, if the density varies with distance from the axis as p = a(x^2 + y^2). Express the result in terms of the cylinder mass.

5. Calculate the volume of the ellipsoid
(x^2/a^2) + (y^2/b^2) + (z^2/c^2) ≤ 1.

Attachments
Purchase this Solution
Solution Summary

In this solution we solve several problems involving multiple integrals.

Solution Preview

Please see the attached file for the complete solution.

1. We wish to evaluate the integral:
(please see the attached file)

where D is the domain given by (please see the attached file) and (please see the attached file)

The easiest way to solve this integral is to transform to polar coordinates. We have:
(please see the attached file)

2. (i) We wish to find the area A of the region D enclosed by the ellipse:
(please see the attached file)

For every point in D, we have:
(please see the attached file) ...

Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

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

Solving quadratic inequalities

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

Exponential Expressions

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

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Vector Calculas and the Applications

    527735 Vector Calculas and the Applications 1.

  • Inner product spaces

    This is a proof of orthogonality and unit vectors, and shows how to determine distance between vectors.

  • Two balls with masses M and m

    By calculas method, the poit is located about which the moment of inertia is minimum and it comes out, x = m*L/(M+m) If we assume that center of mass of M and m at a distance, x1 from M and (L-x1) from m.

  • Mathematics

    331060 Calculas Please show all woCarlos is blowing air into a soap bubble at the rate of 7 cm3/sec. Assuming that the bubble is spherical, how fast is its radius changing at the instant of time when the radius is 11 cm? cm/sec.

  • Vector Subspaces

    I have in my old algebra text a theorem (Elementary Linear Algebra with Applications by W.

  • linear algebra techniques used in computer graphics

    This type of analysis is especially important in imaging, and especially medical applications. How are linear algebra techniques used in computer graphics?

  • What is linear algebra? What is matrix algebra?

    It has extensive applications in the natural sciences and the social sciences, since nonlinear models can often be approximated by a linear one.

  • Verification of the divergence theorem on two given surfaces

    96938 Applications of div, grad, curl: Verification of the divergence theorem on two given surfaces Verify the divergence theorem (∫∫ (F.n) ds = ∫∫∫ (grad.F) dV) for the following two cases: a.

  • Vectors, graphs, and counting

    One uses lottery tickets to explore counting techniques, one discusses graphs of parabolas and hyperbolas, as well as applications of parabolas, and one discusses equivalent vectors.

View More Related Solutions