Exam 7: Additional Topics in Integration

In using Simpson's rule, the number of subintervals n may be chosen to be even.

Thanks to smaller and more fuel-efficient models, American carmakers have doubled their average fuel economy over a 13-year period, from 1974 to 1987. The graph depicted in the figure gives the average fuel consumption in miles per gallon (mpg) of domestic-built cars over the period under consideration ( corresponds to the beginning of 1974). Use the trapezoidal rule to estimate the average fuel consumption of the domestic car built during this period. Round the result to the nearest hundredth. (Hint: Approximate the integral .) Please enter the answer in decimal form. __________ mpg

What function is a probability density function on the interval ?

Evaluate the following improper integral whenever it is convergent.

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

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 5 years since the program was introduced. Round to the nearest integer. __________ people

Approximate the value of the definite integral. Use the trapezoidal rule. Please give the answer to four decimal places. Use the Simpson's rule. Please give the answer to four decimal places.

Use the table of integrals to find the integral.

Use the table of integrals to find the integral.

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 8 A.M. is given by per hour. Determine the number of visitors admitted by noon. Round to the nearest integer. __________ visitors

Evaluate the following improper integral whenever it is convergent.

The amount of snowfall in feet in a remote region of Alaska in the month of January is a continuous random variable with probability density function Find the amount of snowfall one can expect in any given month of January in Alaska. __________ ft

Simpson's rule is more accurate than the trapezoidal rule.

At a certain point, a river is 65 ft wide, and its depth, measured at 5-ft intervals across the river, is recorded in the following table. Here, x denotes the distance (in feet) from one bank of the river and y (in feet) is the corresponding depth. If the average rate of flow through this section of the river is 4 ft/sec, use the Trapezoidal Rule with to find the rate of the volume of flow of water in the river. Hint: Volume of flow = rate of flow area of cross section.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Find the exact value of the integral.

Use the table of integrals to find the integral.

Tracy purchased a 15-year franchise for a computer outlet store that is expected to generate income at the rate of dollars/year. If the prevailing interest rate is 10% / year compounded continuously, find the present value of the franchise. (Hint: Use the formula of the present value .) Please round the answer to the nearest cent. $__________

The microprocessors, which are used in automobiles to regulate fuel consumption, are guaranteed against defects for 20,000 miles of use. Tests conducted in the laboratory under simulated driving conditions reveal that the distances driven before the microprocessors break down are exponentially distributed and that the average distance driven before the microprocessors fail is 120,000 miles. What is the probability that a microprocessor selected at random will fail during the warranty period?

The velocity of a dragster t seconds after leaving the starting line is ft/sec. What is the distance covered by the dragster in the first 11 seconds of its run? Please round your answer to the nearest whole number. __________ ft

Based on data collected during an experiment, a biologist found that the number of fruit flies (Drosophila) with a limited food supply could be approximated by the exponential model where denotes the number of days since the beginning of the experiment. Find the average number of fruit flies in the colony in the first days of the experiment and in the first days. Please round your answers to the nearest integer. The average number of fruit flies in the first days : __________ The average number of fruit flies in the first days : __________