Directions for 8

Directions for 8.1.24 (Determine whether the improper integral is convergent or divergent. Do not evaluate the integral. SHOW WORK)

Directions for 8.2.4 (Find the indefinite integrals and evaluate the definite integrals. In some of the problems a particular change of variable is suggested.)

Directions for 8.3.4 (A function u or dv is given. Find the piece u or dv which is not given, calculate du and v, and apply the Integration by Parts Formula.)

UMGC Q#3 Fall 2020

                                                           University of Maryland Global Campus                                                                    Dr. A Mohamed

                                                          MATH 141 6381 - Calculus II                                                                                                               Fall 2020

                                                                                   Quiz #3 (100 pts)                                                                                                                     09/09/’20

(Show all your work to get full credit) Due: Tuesday, September 15, 2020 @ 11:59 p.m.

1. (30 pts) Find the derivative of these functions.

a. fx=arcsecex2

b. gx=arctanx3

c. hx=lnarctanx3

2. (48 pts) Find the following integrals.

a. x+24-x2dx

b. 1x9x2-16dx

c. 1x2-4x+7dx

d. x3x2-2x+4dx

3. (22 pts) Evaluate these integrals.

a. 01/6 31-9x2 dx

b. 01/2   arcsinx1-x2dx

4. Bonus 10 pts. Find the area under the curve y=11+x2

, above the x-axis

, and between the lines x=0

 and x=12

.