Exam 7: Additional Topics in Integration

Use the table of integrals to find the integral. Hint: First use the substitution u = x + 6. Use C as the constant of integration.

The supply function for the CD manufactured by Herald Records is given by where p is the unit price in dollars and x stands for the quantity that will be made available in the market by the supplier, measured in units of a thousand.Use Trapezoidal Rule (take n = 8) to estimate the producers'surplus if the price is $8/CD.Round answer to two decimal places.

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.

Evaluate the improper integral whenever it is convergent.

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.

Find the indefinite integral.

Use the table of integrals to find the integral.

Find the indefinite integral.

Find a bound on the error in approximating the definite integral using the trapezoidal rule with 8 intervals.

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

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: .)

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 statement is true or false. If f is a polynomial function of degree less than or equal to 3, then the approximation using Simpson's rule is exact.

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

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

The demand function for Apex women's boots is where p is the wholesale unit price in dollars and x is the quantity demanded daily, in units of a hundred.Find the consumers' surplus if the wholesale price is set at $50/pair.

Nine milligrams of a dye (D) are injected into a vein leading to an individual's heart.The concentration of the dye in the aorta measured at 2-second intervals is shown in the accompanying table.Use Simpson's rule and the formula to estimate the person's cardiac output.Round the result to the nearest tenth. __________ L/min

Find the indefinite integral.

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 .

Sales of the latest recording by Brittania, a British rock group, are currently units/week (each unit representing 10,000 discs), where t denotes the number of weeks since the recording's release.Find an expression that gives the total number of discs sold as a function of t.