Calculus Early Transcendentals

Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone if its density function is

Use Stokes' Theorem to evaluate where is the curve of intersection of the plane and the cylinder is oriented counterclockwise as viewed from above.

Set up, but do not evaluate, a double integral for the area of the surface with parametric equations

Use Stoke's theorem to evaluate C is the curve of intersection of the plane z = x + 9 and the cylinder

The temperature at the point in a substance with conductivity is Find the rate of heat flow inward across the cylindrical

Use a computer algebra system to compute the flux of F across S. S is the surface of the cube cut from the first octant by the planes

Assuming that S satisfies the conditions of the Divergence Theorem and the scalar functions and components of the vector fields have continuous second order partial derivatives, find , where a is the constant vector.

Suppose that where g is a function of one variable such that .Evaluate where S is the sphere

Evaluate the surface integral for the given vector field F and the oriented surface S. In other words, find the flux of F across S.

Find an equation of the tangent plane to the parametric surface represented by r at the specified point. ;

Use Gauss's Law to find the charge contained in the solid hemisphere , if the electric field is

Evaluate the surface integral for the given vector field F and the oriented surface S. In other words, find the flux of F across S. in the first octant, with orientation toward the origin.

Use Stokes' Theorem to evaluate where and is the triangle with vertices is oriented counterclockwise as viewed from above.

Use Stokes' Theorem to evaluate is the part of the paraboloid that lies inside the cylinder oriented upword.

Use Stokes' Theorem to evaluate where is the circle . is oriented counterclockwise as viewed from above.

Evaluate the surface integral. Round your answer to four decimal places. S is surface

Evaluate the surface integral. S is the part of the plane that lies in the first octant.

A fluid with density flows with velocity Find the rate of flow upward through the paraboloid

Match the equation with one of the graphs below.

Use the Divergence Theorem to calculate the surface integral ; that is, calculate the flux of across . S is the surface of the box bounded by the coordinate planes and the planes .