MATH 1172 Quiz: MATH 1172 Ohio State University Math 1172 Fa 2014 Quiz 1 Solution

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

Problem 1 [6 points] consider the region r bounded by the graph of y = x + 3 and the x-axis over the interval [ 3, 6]: [3 pts] Set up an integral that represents the volume of the solid whose base is the region r and whose cross-sections perpendicular to the x-axis are semicircles. Solution: as our cross sections are perpendicular to the x-axis, we will integrate with respect to x. Let us construct a formula which gives us the area of the cross section a given value x. The diameter of the semicircle lies on the region. Hence the length of the diameter of the cross section at x is given by d(x) = x + 3 0. Since the radius is half of the diameter and the area of a semi circle is 1 the cross section at x is given by. Our region ranges from x = 3 to x = 6.