Exam 7: Additional Topics in Integration

Use the table of integrals to find the integral. Use C as the constant of integration.

Use the formula to find the integral.

The commissioner of the City of Newton Department of Public Works estimates that the number of people in the city who have been recycling their magazines in year t following the introduction of the recycling program at the beginning of 1990 is Find the average number of people who will have recycled their magazines during the first 3 years since the program was introduced.

Find the area of the region bounded by the x-axis and the graph of the function

The average waiting time for patients arriving at the Newtown Health Clinic between 1 P.M. and 4 P.M. on a weekday is an exponentially distributed random variable x with expected value of 30 minutes. What is the probability that a patient arriving at the clinic between 1 P.M. and 4 P.M. will have to wait between 27 and 32 minutes? Round your answer to two decimal places.

Evaluate the following improper integral whenever it is convergent. Enter divergent if the integral is divergent.

The amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain May day in a city has been approximated by where is measured in pollutant standard index (PSI), and is measured in hours, with corresponding to 5 a.m. Use the trapezoidal rule with to estimate the average PSI between 5 a.m. and noon. Please round the answer to the nearest hundredth. (Hint: .) __________ nitrogen dioxides

Find the indefinite integral.

The supply function for the CD manufactured by Herald Records is given by where p is the unit price in dollars and x stands for the quantity that will be made available in the market by the supplier, measured in units of a thousand. Use Simpson's Rule (take n = 8) to estimate the producers'surplus if the price is $9/CD.(Round your answer to two decimal places)

Use the table of integrals to find the integral. Use C as the constant of integration.

Evaluate the improper integral whenever it is convergent.

National Welding uses industrial robots in some of its assembly-line operations. Management has determined that, on average, a robot breaks down after 1,000 hours of use and that the lengths of time between breakdowns are exponentially distributed. A. What is the probability that a robot selected at random will break down between 300 and 800 hours of use? Round your answer to two decimal places. B. What is the probability that a robot will break down after 1,200 hours of use? Round your answer to two decimal places.

Evaluate the following improper integral whenever it is convergent.

Determine whether the given function is a probability density function on the specified interval.

The management of AstroWorld ("The Amusement Park of the Future") estimates that the number of visitors (in thousands) entering the amusement park t hours after opening time at 10 A.M. is given by per hour. Determine the number of visitors admitted by noon.

Use the table of integrals to find the integral.

The life span (in years) of a certain brand of color television tube is a continuous random variable with probability density function How long is one of these color television tubes expected to last? __________ year(s)

Use the formula to find the integral.

Evaluate the definite integral by using the method of integration by parts.

Evaluate the improper integral if it is convergent.