1. The region in the rst quadrant enclosed by the curves y = 1 ~ m2, :1: = 0 and y = 0 is rotated around the line a: = 1. The volunIe of this solid is 2?\" unitsa. 2. A solid is created when the region bounded by the semicircles y=v16mz y=v4$2 and the xaxis is rotated about the xaxis. What is the volume of this solid? 0 222:117 0 871'2 O 445E577 0 128m 0 Such a solid does not exist. 3. The region enclosed by the curves 3; = :33, y = 0 and a: = 3 is rotated about the x-azis to create a solid. The volume of this solid 4. What is the approximate volume of the solid created when the region under the curve y = m3 on the interval [0, 2] is rotated around the m-axis? 5. What is the approximate volume of the solid created when the region under the curve 31 = sin a: on the interval [0, 7r] is rotated around the x-axis? (Set this up algebraically, but then to evaluate feel free to use a graphing calculator to evaluate the integral.) 6. R denotes the region bounded by the curves y : (:2 ~ 3)2 and y = ln(:e). A solid is created when R is rotated about the line y : 0. What is the volume of this solid? (You may set up and evaluate the integral using a calculator.) O 4.198 9.747 1.551 7. What is the approximate volume of the solid created when the region under the curve 1; : cos :5 on the interval [ %, is rotated around the m axis 7 (Set this up algebraically, but then feel free to use a graphing calculator to evaluate the integral.) 0 1.467 O 2.003 1.568 4.934 6.282