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University of Maryland Global Campus   Dr. A Mohamed

                                                           MATH 141 6381-Calculus II                                                                                                               Fall 2020

                                                                                    Final Exam                                                                                                                              10/11/’20

(Show all your work to get full credit-Due on Tuesday, October 13, 2020 @ 11:59 p.m.)

1. (50 pts) Find the following integrals.

a. sinxcos2x

 dx

 

 

b. x216- x6 dx

 

 

c. 01arcsinx dx

 

 

        

d. 8x3+13xx2+22 dx

 

 

 

e. -∞+∞ex1+ e2x dx

 

    

2. (20 pts)

a. Find the area of the region bounded by the graphs of fx=2- x2

 and gx=x

.

 

 

b. Find the volume of the solid formed by revolving the region bounded by the graph of       fx=sinx

 and the x-axis 0≤x ≤ π

about the x-axis.   

 

               

3. (30 pts)

a. Find the power series for fx= sin2x

.

 

 

b. Find the Taylor series for gx=sinx,

 expanded about x

=π/2

, first nonzero four terms.

 

 

c. Find the power series for fx=

 4x+2

 , centered at 0

. What is the interval of convergence?