Exam 7: Additional Topics in Integration

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

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Please give the answer to four decimal places. ​ ​ Trapezoidal rule: __________ ​ Simpson's rule: __________

Find a bound on the error in approximating the given definite integral using the trapezoidal rule with n intervals. ​ ​ If necessary, round the answer to three decimal places. ​ Find a bound on the error in approximating the given definite integral using the Simpson's rule with n intervals. ​ ​ If necessary, round the answer to five decimal places.

The management of AstroWorld ("The Amusement Park of the Future") estimates that the number of visitors (in thousands) entering the amusement park t hours after opening time at 8 A.M. is given by ​ ​ per hour. Determine the number of visitors admitted by noon. Round to the nearest integer. ​ __________ visitors

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

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

The velocity of a dragster t seconds after leaving the starting line is ft/sec. What is the distance covered by the dragster in the first 11 seconds of its run? ​ Please round your answer to the nearest whole number. ​ __________ ft

Find the area of the region bounded by the x-axis and the graph of the function. ​ ​ __________ sq units

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 9 years since the program was introduced. ​

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

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 t denotes the number of days since the beginning of the experiment. Find the average number of fruit flies in the colony in the first 10 days of the experiment and in the first 29 days.

Find the volume of the solid of revolution obtained by revolving the region bounded by the graphs of the given functions about the x-axis. ​ and

The velocity of a dragster t seconds after leaving the starting line is ft/sec. What is the distance covered by the dragster in the first 12 seconds of its run? Round the answer to the nearest whole number. ​

Find the area of the region under the graph of from to . ​

Evaluate the following improper integral whenever it is convergent. ​ ​

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

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Please give the answer to four decimal places. ​ ​

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 ​A​(​t) is measured in pollutant standard index (PSI), and t is measured in hours, with corresponding to 5 a.m. Use the trapezoidal rule with to estimate the average PSI between 5 a.m. and noon. Please round the answer to the nearest hundredth.

Find the area of the region under the graph of from to .

Evaluate the following improper integral whenever it is convergent. ​ ​