Area and Volume

MATH 252 First Name MINI-EXAM 4 SUMMER 2023 Last Name INITIALS: OSU Student ID # INSTRUCTIONS: (1) Students have a total of 75 minutes to open, download/print, write out full solutions, and upload ONE pdf of the exam to Gradescope. (2) This is designed to be a 50 minute exam. (3) No resources are permitted to be used on this exam. No calculator, no textbook, no internet, etc. (4) Formatting? There is a 5% (2.5 point) deduction for improperly formatted Mini-Exams. (5) To earn full credit for each problem, you need to clearly and neatly show your work or provide a written explanation when appropriate. Partial credit will be awarded for logical, organized progress toward a solution when work is required and shown. Correct answers with no supporting work will not receive full credit. (6) Exam Honor Pledge: This exam must be taken using no resources, as referenced in (3). You may NOT consult nor share information with any other person(s) or external resource(s) until 5 days after the Mini-Exam. Please indicate on your cover page that you acknowledge pledging to abide by these instructions by signing your name. Pledge: 2 MATH 252 MINI-EXAM 4 SUMMER 2023 INITIALS: (1) (10 pts) Set up, but do NOT evaluate, the integral(s) needed to determine the area of the shaded region between the two curves y + 2 = 0.5×2 and y + x3 = 4x by integrating along the x−axis. Use the three points of intersection given: (−2, 0), (−0.5, −1.9), (2, 0). Do NOT Evaluate. No absolute values. A = MATH 252 MINI-EXAM 4 SUMMER 2023 INITIALS: 3 (2) (10 pts) Set up, but do NOT evaluate, the integral needed to find the √ exact volume V of the solid whose base is in the first quadrant bounded by the curve y = 5 + 11×7 , the line x = 0, the line x = 1, and the x-axis, whose cross-section slices are right triangles with bases perpendicular to the x-axis and with each triangle base equal to the height of the triangle. Do NOT Evaluate. V = 4 MATH 252 MINI-EXAM 4 SUMMER 2023 INITIALS: (3) (12 pts) Let R be the shaded region bounded between the curves 2y 2 = x and x2 = 6−2y. Using the Disk/Washer Method, set up (but do NOT evaluate) the integral(s) needed to compute the volume of the solid V formed when rotating R around the vertical line x = 0, the y-axis. Do NOT Evaluate. No absolute values. V = MATH 252 MINI-EXAM 4 SUMMER 2023 INITIALS: 5 (4) (12 pts) Let R be the shaded region bounded between the curves 6 − 2y = x2 aand y = 1+sin(πx). Using the Shell Method, set up (but do NOT evaluate) the integral(s) needed to compute the volume of the solid V formed when rotating R around the vertical line x = −1. Do NOT Evaluate. No absolute values. V = 6 MATH 252 MINI-EXAM 4 INITIALS: SUMMER 2023 (5) (2 pts) Consider the region enclosed between the two graphs rotated about the y-axis. Determine which integration method CAN be represented using only one integral. Select one. Disk/Washer Method Shell Method Neither Method (6) (4 pts) Evaluate completely. Use the formula to find the arc length of the graph of 2 f (x) = (x + 3)3/2 from x = 0 to x = 1. Use exponents/radicals to keep exact. 3 f 0 (x) = ˆ br h i2 0 Arc Length Formula: L = 1 + f (x) dx a L =