Exam 7: Additional Topics in Integration

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 two decimal places. Hint: Use the formula .

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

Evaluate the improper integral whenever it is convergent. If not, enter divergent.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. Please give the answer to four decimal places. Trapezoidal rule:__________ Simpson's rule: __________ Exact value: __________

If f is a polynomial function of degree more than 3, then the approximation using Simpson's rule is exact.

Evaluate the following improper integral whenever it is convergent.

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 912 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. __________ accidents

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 60,000, what will the membership be 3 years from now?

Determine whether the statement is true or false. In using the trapezoidal rule, the number of subintervals n must be even.

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.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. Please give the answer to four decimal places. Trapezoidal rule: __________ Simpson's rule: __________ Exact value: __________

Find the indefinite integral. Hint: Integrate by parts twice.

Find a bound on the error in approximating the given definite integral using (a) the trapezoidal rule and (b) Simpson's rule with n intervals.

Use the formula to find the integral.

Seven 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.

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

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

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.