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1. (10 pts) Evaluate the integral
 
6
2
0
2 3x x dx 
A. 354
B. 45
C. 180
D. 81

Ans-  
6
2
0
2 3x x dx 
=





(Integrating from 0 to 6)
= 180.
Hence, the answer is “C”.
2. (10 pts) Find the average value of the function over the given interval.
 ( ) 2 10, on 10, 5f x x   
A. 5
B. 15
C. 225
D. 30

Ans- The average value of a function is given by integration of ydx divided by x.
∫ ( )


(
=



(integrating from -10 to 5)
=
( ) ( )


= 5.
Hence, the answer is “A”.
3. (10 pts) Evaluate the integral
0
3 sin 2
2
x
dx
  
 
 

A.
3
2


B.
3
2


C.
3 1
2 2


D.
3 1
2 2


Ans- Integrating within the given limits




( integrating from 0 to )
=


( )

=


Hence, the answer is “A”.


4. (10 pts) Find the total area of the region between the curve and the x-axis.
2 6 9; 2 4y x x x    
A.
1
3

B.
2
3

C.
7
3

D.
4
3
Ans- Total area means integration with variable dx within the given limits.
∫...