MATH 3B Midterm: Math 3B Exam 10
Document Summary
Practice for final (i, solutions: gabriel"s horn is a mathematical object taken by rotating the curve y = 1 x around the x-axis for 1 x < . It can be shown (though not by what we have done) that the resulting surface of the horn has in nite area, i. e. , it is impossible to paint the outside of the horn. Find the volume of gabriel"s horn (i. e. , nd how much paint it would take to ll the inside of the horn). This is nding the volume of revolution between the curve y = 1 x-axis from 1 to . Setting this up as an integral we have x and the. This is an improper integral and so we use the techniques of improper inte- gration to nd the answer. 1 x 2 dx(cid:19) t (cid:18) z t t (cid:18) x 1(cid:12)(cid:12)(cid:12)(cid:12) B stants a, b, c. f (x) dx for some con-
