Exam 16: Methods and Applications of Integration

Find the exact area of the region bounded by y = + 1,x = 1,x = 3,and the x-axis.Also sketch the region.

Suppose that the population of a city in 2000 was 25,400 and in 2005 was 27,300.If the exponential law of growth is assumed,what is the expected population in 2010?

If 80% of the initial amount of a radioactive substance remains after 2 hours,find the decay constant and the half-life of the substance.Express your answers in terms of natural logarithms.

The demand equation for a certain product is p = 400 - 2q,where p is the price per unit (in dollars)for q units.If its supply equation is p = q + 100,then the consumers' surplus when market equilibrium is established is

Find the area of the region bounded by the given equations: y = + 6x + 10 and y = x + 6

Determine the value of the constant k so that = 1.

Solve the differential equation = subject to y(-2)= 1,y > 0.

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

Find the present value of a continuous annuity at an annual rate of 6% for two years if the payment at time t is at the annual rate of f(t)= 200 dollars.Express your answer in terms of e.

For a company,the annual sales S (in millions of dollars)t years from now are predicted to be given by Determine the average value of annual sales over the next four years.

Find the area between the graph of y = f(x)= ,and the x-axis on the interval .Use your graphing calculator to see a graph of this area.

Find the area of the region bounded by the curve y = f(x)= - 4x + 3 and the x-axis on the interval .Use your graphing calculator to see a graph of this area.

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

Find the area of the region bounded by the curves y = and y = x + 2 from x = 1 to x = 2.

Either find the value of or show that it diverges.

Use the formula = ln + C to find )

A company performed a marketing study and concluded that there is a potential of 100,000 customers for its product.At the beginning of the study there were 40,000 customers that used the product,and one year later there were 50,000 customers.Determine the number N of customers t years after the beginning of the study if N follows logistic growth.

Find the average value of f(x)= 9 + 1 over the interval .

A yeast culture is growing at a rate of A'(t)= 0.3 where t is the time in hours and A(t)is the amount in grams.Use n = 8 and the trapezoidal rule to approximate the amount the culture grew over the first four hours.

The probability density function for the life span of an electronics part is where t is the number of months in service.Find the probability that the part lasts longer than 6 months.