Purchase Solution

Triple Integral on Specific Solid

Not what you're looking for?

Ask Custom Question

Compute a triple integral over a specific solid that would be very difficult in rectangular coordinates, but easy in parabolic cylindrical coordinates, u, v, z, where
x=(1/2)(u^2-v^2) y=uv z=z

You must come up with the solid. Remember that the Jacobian determinant (u^2+v^2) must be used when transforming an integral to this coordinate system"

The function of the solid should be given in Cartesian coordinates, and please show the work done to convert to parabolic cylindrical coordinates and to compute the actual integral. It should also include a graph of the solid.

Purchase this Solution
Solution Summary

This shows how to construct a triple integral for a solid for the given conditions. A triple integral over a specific solids are determined.

Solution Preview

Please find the attached solution.

Mathematics, Calculus
Year 4
Triple Integral

Compute a triple integral over a specific solid that would be very difficult in rectangular coordinates, but easy in parabolic cylindrical coordinates, u, v, z, where
x=(1/2)(u^2-v^2) y=uv z=z

You must come up with the solid. ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

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

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.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

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

View More Free Quizzes
Related BrainMass Solutions

  • Evaluate the tripe integral over the solid tetrahedron

    Triple integral xydV over E where E is the solid tetrahedron with vertices (0, 0, 0), (0, 1, 0), (1, 1, 0), and (0, 1, 1) Please see the attached file for detailed solution. It shows how to evaluate a triple integral over the solid tetrahedron.

  • Triple Integrals : Volume of a Solid in Spherical Coordinates

    78440 Triple Integrals : Volume of a Solid in Spherical Coordinates Consider the solid inside the surface X^2 + Y^2 +Z^2 = 9 and outside the surface X^2 +Y^2 +Z^2 = 1 a) Use SPHERICAL coordinates to to write the integral to calculate the volume of

  • Gravitational Attraction : Triple Integral

    28511 Gravitational Attraction : Triple Integral Find the gravitational attraction of a solid hemisphere of radius a and density 1 on a unit point mass placed at its pole REVIEW: Fz=G*triple integral of density*cos(phi)sin(phi)d(rho)d(phi)d(theta

  • Volume of solid, triple integral, sperical coordinates

    186587 Volume of solid, triple integral, sperical coordinates Use spherical coordinates (iterated triple integral) to find the volume of the solid in the first octant whose shape is determined by the graph of the cone z=sqrt(x^2+y^2), the cylinder x^2

  • application of triple and double integrals

    The integration limits are: The integral is then The solution shows how to find the volume of solid using double and triple integrals step-by-step.

  • Triple integrals and volume

    237173 Triple integral Use a triple integral to find the volume of the given solids. 1.)the tetrahedron bounded by the coordinate planes and the plane 2x + 3y + 6z = 12 2.)the solid enclosed by the parabolas z = x^2 + y^2 and z= 0 and x

  • Center of mass of cone, cylindrical coordinate system

    The coordinates of the center of mass x', y', z' are given by the expressions x'=(1/M)*(Triple integral over E of) x*rho dV, y'=(1/M)*(Triple integral over E of) y*rho dV, z'=(1/M)(Triple integral over E of) z*rho dV, where rho is the (posible

  • Triple Integrals : Finding Volume of Solids with Boundaries

    10072 Triple Integrals : Finding Volume of Solids with Boundaries 1) Evaluate the triple integral e^(1-(x^2)-(y^2)) dxdydz with T the solid enclosed by z=0 and z= 4-(x^2)-(y^2) 2) Find the volume of the solid bounded above and below by the cone (z^

  • Seven Calculus Problems

    Use an iterated integral to find the area of a region... 2. Evaluate the double integral... 3. Use double integral to find the volume of a solid... 4. Verify moments of inertia... 5. Limit of double integral... 6. Surface area... 7.

View More Related Solutions