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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. *sinx**cos**2**x*

*dx*

b. *x**2**16- **x**6** dx*

c. *0**1**arcsinx dx *

d. *8**x**3**+13x**x**2**+2**2** dx*

e. *-∞**+∞**e**x**1+ **e**2x** dx*

**2. **(20 pts)

a. Find the area of the region bounded by the graphs of *f**x**=2- **x**2*

and *g**x**=x*

.

b. Find the volume of the solid formed by revolving the region bounded by the graph of * f**x**=**sinx*

and the x-axis *0≤x ≤ π** *

about the x-axis.

**3. **(30 pts)

a. Find the power series for *f**x**= **sin**2**x*

.

b. Find the Taylor series for *g**x**=sinx,*

expanded about *x*

=*π/2*

, first nonzero four terms.

c. Find the power series for *f**x**=*

*4**x+2*

, centered at *0*

. What is the interval of convergence?

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