Exam 7: Additional Topics in Integration

The number of streets in the downtown section of a certain city that need repairs in a given year is a random variable with a distribution described by the probability density function Find the probability that at most half of the streets will need repairs in any given year.

Evaluate the following improper integral whenever it is convergent.

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?

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

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

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

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

What function is a probability density function on the interval ?

Evaluate the following improper integral whenever it is convergent.

Use the table of integrals to find the integral.

Use the table of integrals to find the integral.

Find the indefinite integral.

Find the indefinite integral.

Determine the value of the constant k so that the function is a probability density function on the interval .

The microprocessors, which are used in automobiles to regulate fuel consumption, are guaranteed against defects for 15,000 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 80,000 miles.What is the probability that a microprocessor selected at random will fail during the warranty period? Please round the answer to the nearest hundredth.

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

Evaluate the following improper integral whenever it is convergent.

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

Find the area of the region under the graph of from x = 1 to x = 9.

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