To prepare for this discussion, read the instructor guidance, and Sections 2.2, 2.3, 2.4, 3.3, “Steps” in Section 3.4, 3.5, 4.3, and Chapter 5 of the Newman (2016) textbook. In contrast to qualitative

MAC 2312 Calculus 2 Quiz 1 Welcome to your first Quiz! For all questions, please show your work. This allows me to provide helpful feedback and appropriately assign partial credit. Correct answers without supporting work will not receive credit. 1) Find the exact area bounded by = −2+ 9 and = 1 22− 6− 9. Do not give a decimal answer. 2) Find the exact area of the region bounded by = 2 and = √ for 0≤ ≤ 4. Do not give a decimal answer. 3) For the following problems, SET UP - BUT DO NOT INTEGRATE the Integral representing the volume generated by rotating the region bounded by the given curves between = −1 and = 1 about the indicated axis USING THE DISC/WASHER METHOD The functions are: = √2 3 and = 1 x axis ______________________________________________________ y = -1 ______________________________________________________ y = 1 ______________________________________________________ 4) For the following pr oblems, SET UP - BUT DO NOT INTEGRATE the Integral representing the volume generated by rotating the region bounded by the given curves about the indicated axis USING THE SHELL METHOD = 2, = 2− 2, and ≥ 0 y axis ______________________________________________________ x = -2 ______________________________________________________ x = 1 ______________________________________________________ 5) Find the volume of the solid obtained by rotating the re gion bounded by = −2+ 6− 8 and = 0 about the y -axis. 6) Find the volume of the solid obtained by rotating the region bounded by = −2+ 6− 8 and = 0 about the x -axis. 7) Find the volume of the solid obtained by rotating the region bounded by = (− 3)2 and = 4 about = 1.