Exam 16: Methods and Applications of Integration

The velocity of an object is given by V(t)= ,where t is the time in seconds and V(t)is the speed in feet/sec.Use n = 6 and Simpson's rule to approximate the distance moved over the interval .

=

Use the tables to find: dx

Use the tables to find:

The demand equation for a certain product is p = 200 - ,where p is the price per unit (in dollars)for q units.If its supply equation is p = 6q + 160,find the consumers' surplus and the producers' surplus when market equilibrium has been established.

The population N of a certain city follows the law of exponential growth given by N = where and k are constants and t is the number of years past 1965.In 1965 the population was 10,000 and in 1985 it was 30,000.What is the expected population in 2005?

Use the formula = - ln + C to find

Use definite integrals to find the area between y = - ,the x-axis,x = -1,and x = 1.

The growth rate of a tumor satisfies = 0.2V ,where t is the time in months and V is the volume in cubic millimeters.If the initial volume is 1.86 millimeters,find V as a function of t.

Use the table below to determine dx.Indicate the formula number employed. I. + C II. + C III. + C IV. + C

Use the table below to determine dx.Indicate the formula number employed. I. + C II. + C III. + C IV. + C

The population of a town has exponential growth.In 1976 the population was 10,000 and in 1986 it was 20,000.If N is the population at time t,where t is the number of years after 1976,and if you assume than ln 2 = 0.7,then

If 55% of the initial amount of a radioactive sample remains after 10 hours,find the decay constant and the half-life of the element.

Use the table below to determine dx.Indicate the formula number employed. I. + C II. + C III. + C IV. + C

Determine if converges or diverges.If it converges,to what number does it converge?

Use the trapezoidal rule with n = 4 to estimate the value of

Solve the differential equation y' = (2x + 1)subject to the condition that y(-1)= .

Use the formula = - ln + C to find .

Express the area of the shaded region in terms of an integral (or integrals).Do not evaluate the expression:

The amount A of glucose present in the bloodstream at any time t is governed by the differential equation where R and k are constants.Find A as a function of t.