Calculus 2

UTSA, Math 1224, Calculus II Spring Semester, 2015 Homework 1

Due February 02, 2015

Instructor: Dr. Ivanka Stamova

Student Name: …………………………………………………

1. (1 point) Find the derivative )( '

xg , if

(a)   

xx

x t

dt xg

cot

sin 1

)( ; (b)  



3

3 352

arccos)(

xx

xx

dttxg

2. (5 points) Evaluate the integrals

(a) dx xx

2

31 csc

2

31 cot

  ; (b) 

 dt

t

t

22/3 )1(

6 ;

(c)  

6 )83( x

dx ; (d) 

 24 1arcsin xx

dx ;

(e) dx xx

  3

2 1

2 ; (f) dx

xx 

23

2

23

2 csc

2 tan





;

(g)  dxxxx  1

0

3 2 1253 ; (h) 



4/23

0 2

49 x

dx ;

(i) dx xxx

xx 



 1

0 24

3

9126

33 ; (j) 



2

3/2 2

1

)seccos(

xx

dxxarc

Total: 6 points