Exam 7: Additional Topics in Integration

The number of voters in a certain district of a city is expected to grow at the rate of people per year years from now.If the number of voters at present is , how many voters will be in the district years from now? Please round your answer to the nearest integer. __________ people

Consumer spending in dollars per person on media and entertainment from 2004 through 2009 is given in the following table. Use the Trapezoidal Rule with n = 5 to estimate the average yearly spending by consumers on media and entertainment over the period in question.Round answer to two decimal places.

Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval.

Evaluate the following improper integral whenever it is convergent.

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

Find the area of the region under the curve over the indicated interval. __________ sq units

Use the table of integrals to find the given integral.

The membership of the Cambridge Community Health Plan (a health maintenance organization) is projected to grow at the rate of thousand people/year, t years from now.If the HMO's current membership is 40,000, what will the membership be 4 years from now? __________ people

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

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

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

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.

Find the indefinite integral.

Find the area of the region under the given curve over the indicated interval.

Find the indefinite integral.

Evaluate the improper integral if it is convergent.

Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval.

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 600 hours of use? Round your answer to two decimal places. b.What is the probability that a robot will break down after 1,100 hours of use? Round your answer to two decimal places.

Use the table of integrals to find the integral.