Find the volume of the wedge cut from the first octant by the cylinder and the plane . Evaluate Evaluate Find the centroid of the region in the first quadrant bounded by the axis, , and , if . x Find, where is the region in the first octant bounded by and the plane . E Find the volume of the region between the cylinder and = 0, bounded by the planes z = 0, = 1, = -1 and = 1. x x y y Set up an integral for the volume of the solid bounded by the cylinders and, below by = 0, above by , using either spherical or cylindrical coordinates. z Set up the integral for the volume of the solid bounded below by the sphere and above by . Hint: you might find it useful to get a rectangular equation for the sphere. Chapter 14 Find the rate of change of in the direction of at the point (3,2,6)
Find the volume of the wedge cut from the first octant by the cylinder and the plane . Evaluate Evaluate Find the centroid of the region in the first quadrant bounded by the x axis, , and , if . Find, where E is the region in the first octant bounded by and the plane . Find the volume of the region between the cylinder and z = 0, bounded by the planes x = 0, x = 1, y = -1 and y = 1. Set up an integral for the volume of the solid bounded by the cylinders and, below by z = 0, above by , using either spherical or cylindrical coordinates. Set up the integral for the volume of the solid bounded below by the sphere and above by . Hint: you might find it useful to get a rectangular equation for the sphere. Chapter 14 Find the rate of change of in the direction of at the point (3,2,6)