Exam 7: Additional Topics in Integration

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

Find the indefinite integral.

Use the formula to find the integral.

In a submerged trial run of an attack submarine, a reading of the submarine's velocity was made every quarter hour, as shown in the accompanying table.Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period.Please round the answer to the nearest hundredth if necessary.

As a result of increasingly stiff laws aimed at reducing the number of alcohol-related traffic accidents in a certain state, preliminary data indicate that the number of such accidents has been changing at the rate of accidents/month t months after the laws took effect.There were 982 alcohol-related accidents for the year before the enactment of the laws.Determine how many alcohol-related accidents were expected during the first year the laws were in effect.Please round the answer to the nearest integer.

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

Find the indefinite integral.

a.Determine the value of the constant k so that the function is a probability density function on the interval . __________ b.If x is a continuous random variable with the probability density function given in part (a), find the probability that x will assume a value greater than 1. Round your answer to four decimal places.

Suppose the time intervals between arrivals of successive cars at an expressway tollbooth during rush hour are exponentially distributed and that the average time interval between arrivals is 8 seconds.Find the probability that the average time interval between arrivals of successive cars is more than 17 seconds. Round your answer to two decimal places.

The quantity demanded x (in thousands of pounds) of a certain brand of butter each week is a continuous random variable with probability density function What is the expected demand for this brand of butter each week? __________ lb

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 : __________

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.

Use the table of integrals to find the integral.

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

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 amount of time t (in seconds) it takes a motorist to react to a road emergency is a continuous random variable with probability density function What is the expected reaction time for a motorist chosen at random?

Use the table of integrals to find the given integral.

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

The quantity demanded x (in thousands of pounds) of a certain brand of butter each week is a continuous random variable with probability density function What is the expected demand for this brand of butter each week?