For 2a

For 2a. find the volume of the solid formed by revolving the region R bounded by f(x) = 2-2x and g(x) = 1 about the line y=1. Thanks.

University of Maryland Global Campus                    Dr. A Mohamed

                                                          MATH 141 6381 - Calculus II                                                                                                               Fall 2020

                                                                                   Quiz #2 (100 pts)                                                                                                                     09/02/’20

(Show all your work to get full credit) Due: Tuesday, September 8, 2020 @ 11:59 p.m.

1. (20 pts) Find the area of the region bounded by the graphs of

a. x=3-y2

 and x=y+1

b. fx=3x3-x2-10x

 and gx=-x2+2x

2. (28 pts) Find the volume of the solid formed by revolving the region R

 bounded by

a. fx=2-x2

 and gx=1

 about the line y=1.

 (Disk method)

b. y=x

  and y=x2

 about the x-axis

. (Washer method)

3. (26 pts) Find the length of these curves.

a. fx=23x3/2+1

 on the interval 0 , 1

.

b. Find the arc length of the graph of y=ln?(cosx)

 from x=0

 to x=π/4

4. (14 pts) A force of 750 pounds compresses a spring 3 inches from its natural length of 15 inches.

a. Find the spring constant (Use Hook’s law)

b. Find the work done in compressing the spring an additional 3 inches.

5. (12 pts) Find the center mass of a system of point masses m1=6 ,   m2=3 ,   m3=2 ,    m4=9

 located at 3 , -2 ,   0 , 0 ,   -5 , 3 ,   4 , 2

.

6. Bonus question (10 pts) Find cosx+sinx2dx