Be sure to Show all your work and clearly indicate your nal answer. Word problems should be answered in complete sentences. Please follow these markers: [C] - You should use a computer to either graph (e.g. on geogebra3d) or do calculations I can't expect you to do by hand (e.g. on wolframAlpha). Do not use a computer or calculator on problems without this symbol. Doing so is a violation of academic integrity. [P] - A picture is required to receive full credit for this problem; the picture should be labeled with relevant information. [S] - Your answer needs to be given in the form of a complete sentence, with units where applicable. (4:) - This question is optional, but is good practice and might provide some interesting ideas. Be sure to practice your homework. If you struggled with a problem the rst time, do it again and you should struggle less. Keep doing the problem until it makes as much sense as the problems you understood the rst time around. The homework sets build on each other; many skills practiced in this homework will be called upon in future homework and exams. Do not use any formulas not discussed during class, including any formulas you have learned in physics [chemistry / etc. classes. You will not receive credit for using those formulas. The solutions for all integrals must include a sketch of the domain. Homework 8 Learning Objectives: Upon completing this homework, you should feel comfortable with the following skills. 0 Able to set up and evaluate double integrals in rectangular coordinates o Able to set up and evaluate triple integrals in rectangular coordinates o Able to properly utilize symmetry to simplify integrals o Able to use integrals to calculate areas or volumes 0 Understanding the relationship be densities (eg. mass density, population density, etc.) and integration 0 Using an integral to calculate the average value of a function 1. [Double Integrals on Rectangular Regions] Evaluate the following double integrals. Be sure to indicate in your sketch of the region whether you are integrating row-byrow or column-by-column. (In some cases, one order of integration will be much easier than the other, so choose wisely.) (a) ff(1+2myaldA,WhereR=Og;cg3,0Sygl a _ _ a _ _ (b) j](6$3y2+4ay) dA, whereR=1<:r u r i msin da where r: s y g and mass the density of a thin metal plate on d it x is given by p in kg if we want total to be what should make value k integrals general regions evaluate following double integrals. sure indicate your sketch region whether you are integrating row-byrow or coluinn-bycolurnn. some cases one order integration will much easier than other so choose wisely. e rectangular whose vertices till t triangular my2 trapezoid with y3 bounded .t="0," set up simplify them using symmetry do not have them. j sm for below determine positive negative zero explain reasoning. don need answer this question. use integral calculate areas. area area. :c='y\".' integral: cos dardy w m population city units distance miles. hundreds people mi. can pmm="m+w" find lowest highest. number who live city. as triple coordinates. solid block occupies a: z has lung block. gas a. concentration c are2 y2 moi moles region. volume homework selected answers zero. positive. negative. coil sin maximum highest at approx. people. roughly>