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Let be a constant vector. Verify that the moment of inertia of a spherical shell of uniform density about its diameter is where is the mass and is the radius.

Let be defined on an op disk You want to show that if and have continuous first partial derivatives a then is conservative. C ex cos 2y dx 2ex sen2y dy r 1 cos C: Think About It of the surface It En los ejercicios 29 y 30, hallar el flujo de F sobre la superficie cerrada. Three particles move from the point to the point along different paths. Dob,es of vector fields include velocity fields, electromagnetic fields, and gravitational fields. Graph and find the area of one turn of the spiral ramp donde y Se quiere demostrar que si M y N tienen primeras derivadas parciales continuas y entonces F es conservativo.

Work Consider a particle that moves through the force field from the point to the point along the curve Find the value of such that the work done by the force field is 1. To embed a widget in your blog’s sidebar, install the Wolfram Alpha Widget Sidebar Pluginand copy and paste the Widget ID below into the “id” field: Think Ttriples It In Exercises 17—20, determine how the graph of the surface differs from the graph of see figurewhere and It is not necessary to graph s.

In hydrodynamics the study of fluid motiona velocity field that is divergence free is called incompressible. Explain your ordering without doing any calculations.

In Exercises 21—26, evaluate the line integral along the given path s. Utilizar la segunda forma alternativa del teorema de Green y la propiedad The expressions and are the derivatives in the direction of the outward normal vector of and are defined by and F sen sen Usar la ley de Gauss para hallar la carga total que hay en el interior de la superficie cerrada formada por el hemisferio y su base circular en el plano xy.

### Wolfram|Alpha Widgets: “Calculo de integrales dobles, triples” – Free Widget Gallery Widget

Give some physical examples of vector fields. In Exercises 1 and 2, compute and sketch several representative vectors in the vector field. Consider a single heat source located at the origin with temperature a Calculate the heat flux across the surface as shown in the figure.

How does the area of the ellipse compare with the magnitude of the work robles by the force field on a particle that moves once around the ellipse see figure? Moment of Inertia In Exercises 33 and 34, use the following formulas for doblea moments of inertia about the coordinate axes of a surface lamina of density Para comprobarlo, sea y donde Como se deduce que F es conservativo.

Esto se muestra en el ejemplo 9.

## Calculadora de integrales dobles

El cable se encuentra a lo largo de y su densidad es Si esto es posible, S es una superficie orientada. The sphere where and You will then see the widget on your iGoogle account. Consecuentemente, el trabajo realizado por F a lo largo de una curva suave C desde A hasta B es como se muestra en la figura Por ejemplo, esferas, elipsoides y paraboloides son suaves, mientras que el cono del ejemplo 3 no es suave.

In Exercises 7—18, use the Divergence Theorem to evaluate and find the outward flux of F through the surface of the solid bounded by the graphs of the equations.

## Cap15 Análisis Vectorial

Open-Ended Project The parametric equations where and represent the surface shown below. Si Q tiene una superficie lateral como en la figura Definir un campo vectorial en el plano y en el espacio.

Ver la figura It runs from triplds position to a point on the ground 50 meters from the base of the installation where they are located. Find the work done by the force that keeps the stone moving in a circular path. The expressions and are the derivatives in the direction of the vector N and are defined by The part of the cylinder where and Discuss the orientation of the curve and its effect on the value of the integral.

Enunciar el teorema de Stokes. El toro donde y Con estas restricciones sobre S y Q, el teorema de la divergencia es como sigue. On the other hand, Consequently, Similarly, you can use and to show that By adding the integrals and you obtain the conclusion stated in the theorem. In Exercises 57—62, determine whether the vector field F is conservative.

The iteraeas o Una superficie orientable S tiene dos caras. Work To allow a means of escape for workers in a hazardous job 50 meters above ground level, a slide wire is installed.

Compare the result with the work required to move the object along the straight-line doblws connecting the points. Figure for 7 Figure for 8 8.