calculus integration homework

HOME WORK #2, MATH 112, SEM. 362 1/9

JUBAIL UNIVERSITY COLLEGE

SEMESTER 362

MATH 112, Homework # 2 Date of submission: 27/04/2016

Name: _________________________________________ ID:________________ Section: 201_

1. Find dy

dx .

a. 4

2 3 cosh

1

x y

x

    

 

b.  1ln sinhy x

c. 1cscy h x

    

 

HOME WORK #2, MATH 112, SEM. 362 2/9

2. Evaluate the given integral by using appropriate method of integration.

a. 2

2

2 3

3 2



  x

dx x x

b.    

2

2 2

2 10 4

2 3

 

  x x

dx x x

HOME WORK #2, MATH 112, SEM. 362 3/9

c. 3 2 2ln( )x x dx

d.  cos ln x dx

e. 2 3 x

x e dx

\

HOME WORK #2, MATH 112, SEM. 362 4/9

f.  

2

3

1

1 

 dx

x

g. 0

4 3  

 x

x

e dx

e

h. 4

tan sec x x dx

HOME WORK #2, MATH 112, SEM. 362 5/9

i. 3

2

3

4  x

dx x

j. 2

16

 x

dx x

k. 2

4  dx

x x

HOME WORK #2, MATH 112, SEM. 362 6/9

3. Approximate the integral using (a) the trapezoidal approximation 4

T

(b) Sampson’s approximation 6

S

3

1

1

3 1 dxx

4. Show that   0

1 2 ; 4 6

3

k

k

x if x x





    

HOME WORK #2, MATH 112, SEM. 362 7/9

5. Show that the given sequence is strictly increasing or strictly decreasing.

a. 13 4 n

n

n





   

 

b.  2 1

n

n ne

 



c. 1

5

!

n

n n





     

HOME WORK #2, MATH 112, SEM. 362 8/9

6. Determine whether the series converges.

a. 1

1

3

5 k

k









b. 2

2

k

k











HOME WORK #2, MATH 112, SEM. 362 9/9

7. Determine whether the sequence converges; if so find its limit.

   2

1

1 3

3 n

n n

n





      

8. Find the general term of the sequence.

1 1 1

1, , , 4 27 256

 