Math& 152 Spring 2023 "Applications of Integration" Challenge Set INSTRUCTIONS: Please do your work on a separate sheet or sheets of paper. To receive full credit, :1 problem must be solved correctly and completely, with all relevant work shown; solutions should be clear, concise, and thorough Use complete sentences as appropriate Sloppy or incomplete work will not receive full credit, even if the solution is correct. You are strongly encouraged to make use of rough draIts before writing up your nal submission. 1. Find the area between the curves 3; = :I:2 and y = S two ways: First sat up and compute an integral with respect to :2: Then set up and compute an intcgral with mama to y 2. Find the area between the curves y = x2 and y = '12: + l on the interval [1.1] 3. Find the center of mass of the region bounded by the curves 1; = :2 and y = ..":"i + l. 4. Find the volume of the solid produced by rotating the region bounded by the curves y=zgandy=13+laroundthe1iney=37 5. Find the volume of the solid produced by rotating the region bounded by the curves y=xzandy=ra+laroundthelinex=1 Math: 15-2 "Applications of Integration" Challenge Set [END OF SET]