Exam 7: Additional Topics in Integration

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 seven 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 seven decimal places.

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.

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

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

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.

Find the indefinite integral.

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

Determine whether the statement is true. If exists, then exists and . Answer yes or no.

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

Use the formula to find the integral.

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

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 the indefinite integral.

Find the area of the region under the graph of from x = 1 to x = 2.

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

The revenue of Virtual Reality, a video-game arcade, is generated at the rate of dollars. If the revenue is invested t years from now in a business earning interest at the rate of 18% / year compounded continuously, find the accumulated value of this stream of income at the end of 2 years . Round to the nearest dollar. $__________

National Welding uses industrial robots in some of its assembly-line operations. Management has determined that, on average, a robot breaks down after 1,000 hours of use and that the lengths of time between breakdowns are exponentially distributed. a. What is the probability that a robot selected at random will break down between 300 and 600 hours of use? Round your answer to two decimal places. b. What is the probability that a robot will break down after 1,100 hours of use? Round your answer to two decimal places.

Evaluate the following improper integral whenever it is convergent.