Exam 7: Additional Topics in Integration

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

Find the indefinite integral.

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-foot intervals. Using Simpson's rule with , estimate the surface area of the lake. Round the result to the nearest tenth. __________

Evaluate the following improper integral whenever it is convergent.

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

Use the table of integrals to find the given integral.

Evaluate the following improper integral whenever it is convergent.

In a study conducted by a certain country's Economic Development Board regarding the income distribution of certain segments of the country's workforce, it was found that the Lorentz curve for the distribution of income of college professors is described by the function Compute the coefficient of inequality of the Lorentz curve. Round to the nearest thousandth. Hint: Use the formula .

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

Find the indefinite integral.

Use the table of integrals to find the integral.

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

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.

Determine the value of the constant so that the function is a probability density function on the interval . If is a continuous random variable, compute the probability that will assume a value between and .

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

Find the indefinite integral.

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.

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 7 a.m. Use the trapezoidal rule with to estimate the average PSI between 7 a.m. and noon. Please round the answer to the nearest hundredth. (Hint: .)

Evaluate the following improper integral whenever it is convergent.