Calculus homework

MA 141 Turn in Homework 6.4

Name _________________________

1. (#8) Find the area of the region under the graph of the function 2( ) 4f x x x  and above the x-axis over the

interval [0,4]

2. (#16) Find the area of the region under the graph of the function ( ) xf x e x  and above the x-axis over the

interval [1, 2]. Give both the exact answer and the answer rounded to two decimal places.

3. (#24). Evaluate the definite integral

4

1 udu

4. (#32) Evaluate the definite integral 2

0 ( 4)( 1)x x dx 

5. Evaluate the definite integral

2 2

21

1u u du

u

      

 (Find the exact answer.)

6. (#34) Evaluate the definite integral

1 2 2

1 ( 1)x dx

 

7. Evaluate the definite integral 2

1

4 (2 3 )xx e dx

x   . Give both the exact answer and the answer rounded to two

decimals.

8. (#42) The management of Ditton Industries had determined that the daily marginal revenue function associated with

selling x units of their deluxe toaster ovens is given by '( ) 0.1 40R x x   . Where '( )R x is measured in

dollars/unit.

a.) Find the daily total revenue realized from the sale of 200 units of the toaster oven.

b.) Find the additional revenue realized when the production (and sales) level is increased from 200 to 300 units.

9. (#46) Tempco Electronics, a division of Tempco Toys, manufactures an electronic football game. An efficiency study showed that the rate at which the games are assembly by the average work t hours after staring work at 8 a.m.

is . 23 6 20 (0 t 4)

2 t t     Units/hour.

a.) Find the total number of games the average worker can be expected to assembly in the 4-hr morning shift.

b.) How many units can the average worker be expected to assemble in the second hour of the morning shift?

10. A company manufactures x HDTV’s per month. The monthly marginal profit (in dollars) is given by:

'( ) 165 0.1 (0 4,000)P x x x    . The company is currently manufacturing 1,500 HDTV’s per month, but is

planning to increase production. Find the change in the monthly profit if monthly production is increased to 1,600

HDTV’s.