Calculus III, Section 3 Summary

To see a review click on     Section 3 Summary   To see sample solutions, click on     Section 3 Sample Solutions    

Cylindrical & Spherical Coordinates

Example 1. Suppose we want to evaluate     where is the solid enclosed by the planes and and the cylinders We can use the cylindrical […]

Multiple Integrals Additional Problems

Evaluate each one of the following:     Use triple integral to find the volume of the tetrahedron bounded by in the first octant. Use triple […]

Surface Area Problems

Find the surface area of a plane in first quadrant. Find the surface area of over Find the surface area of over the unit disk. Find […]

Surface Area

Example 1. Suppose we would like to find the surface area of that lies above the region bounded by the -axis, -axis and the line . […]

Polar Coordinates Double Integrals Problems

Find the volume of the object below over the region bounded by . Find the volume of the object below over the region bounded by . […]

Polar Coordinate and Double Integral

Example 1. Suppose we are given (1)   where is the region bounded by portion of the unit disk in first quadrant. We know (2)   […]

Double Integral Problems

Find the volume of a solid with height and base a region bounded by and in the first quadrant. Find the volume of the solid below […]

Multiple Integration Introduction

Example 1. We are given the integral (1)   Note that we are integrating the function over the region bounded by (2)   Integrating with respect […]