University:
University of Central Florida
Course:
MAC 2312 | Calculus with Analytic Geometry II
Academic year:

2023
Views:

420

Pages:

7
Author:

Maria

Find the solid's volume with a base in the first quadrant(s) bounded by y = 18-2x and the x-axis using square Q1: cross-sections perpendicular to the x-axis. Enter the answer using exact values 3 0-18-2x2 (18-2x²) dx 2 2x=18 2 x²= 9 x=-3,3 (324-72x²+4x²) dx [324x-24x²+4x5] 12 = [324(3)-24(3)3 + 4 (3)5] - [324(0)-24(0)+(0)] 5 2592 units 5 Find the volume of the solid whose base is in the first and second quadrant(s) bounded by y = 28-7x and the x-axis using square cross-sections perpendicular to the x-axis. Enter the answer using exact values. 0=28-7x2 7x2= (28-7x²)dx = 28 ×4=2>x=±2 -2 2 = 784-392x²+49xdx -2 =784x392x² + 49 x² ** 12 = 784(2) - 392 (2') +42 (2)5) - [784(-2) - 392 (2') + 4 (25)] 49 S Q3. The base of a solid is in the first quadrant bounded above by y = 5 and below by y = 3x between x = 0 andx = 5. Calculate the volume of the solid if the cross-sections perpendicular to the taxis are squares. Enter answer using exact values (5-√5x)dx 25-10752 + 5xdx = 5 §25-10555+5xdx 0 0 = 25x-10052+ x² 15 2 3 0 = 25(5)-2055 (52) + (52)= 125 units The base of a solid is in the first quadrant bounded above by x = 6 and below by y = sqrt(4x) gamma*x = 0 x = 9 . Calculate the volume of the solid if the cross-sections perpendicular to the s-axis are squares. Enter answer using exact The base of a solid is in the first quadrant bounded above by y = 8 and below by y = sqrt(8x) between x = 0 and x = 8 Calculate the volume of the solid if the cross-sections perpendicular to the xaxis are squares. Enter answer using exact values. Define as the region that is bounded by the graph of the function g(y) = 2sqrt(y + 4) the y-axis ,y=-1 y = 2 Use the disk method to find the volume of the solid of revolution when is rotated around the y-axis. Submit an exact answer in terms of Define R as the region that is bounded by the graph of the function f(x) = - 3sqrt(3sin(x)), mex * sin x = pi/x Q7 Use the disk method to find the volume of the solid of revolution when R is rotated around the axis Submit an exact answer in terms of