Math 1B  Calculus II  Chapter 6 test (2)  fall ’06          Name______________________

Show your work for credit.  Write all responses on separate paper. 

1.      Find the average value of  on .
Recall that  

 

2.      Show that the values of c that satisfy the mean value theorem for integrals for the function  on the interval [0, 2] satisfy the equation .

3.      A submarine in the Salton Sea is completely submerged.  The submarine has a circular port hole (window) on the side with diameter 0.5 meter.  Approximate to the nearest hundredth of a Newton the hydrostatic force on the window if its top edge is at depth 1.75 m and its bottom edge is at depth 2.25 m.  Use 1.29*10^3 kg/m^3 as the mass density of saltwater.  Draw a diagram and show your coordinate system.

4.      A cylindrical gasoline tank of radius 2 m and length 6 m is buried 3 meters below the ground as shown in the diagram.  Assume the force density of gasoline 7800 N/m^3.  Introduce a coordinate system and set up (you don’t need to evaluate) an integral to compute the work needed to pump the gas out the tank to ground level.

                                 

 

5.      Set up integrals to find the centroid of  region in the first quadrant below the function .

 

6.      Set up an integral to compute the probability that a normally distributed random variable with mean 40 and standard deviation 10 is greater than 55 and approximate to the nearest thousandth.