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
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.