MATH-M 311 Lecture Notes - Lecture 21: Level Set, Unit Circle, Parallelogram
Document Summary
Section 15. 5 notes- volume and surface area with double integrals. Volume: recall if is nonnegative on , then is area between graph of and -axis, similarly, if inside a region , then is volume between graph of and -plane. Notice it forms a tetrahedron in front of the origin; it is bounded by the , , and planes. Ex: can express as ; base is triangle with vertices , , and, to find volume under tetrahedron, integrate as either type of region, as type i: Find the volume of the tetrahedron formed by , , , and : find equation of plane ( outer face ): Plane: triangle base: between , , and. Calculate the volume of the hoof of the cube in terms of . Find equation of outer face to integrate value only changes with (not tilted at all); when going in direction, go in direction. Volume of whole cube: this is always true: ex.
