Exam 7: Additional Topics in Integration

At a certain point, a river is 65 ft wide, and its depth, measured at 5-ft intervals across the river, is recorded in the following table. Here, x denotes the distance (in feet) from one bank of the river and y (in feet) is the corresponding depth.If the average rate of flow through this section of the river is 4 ft/sec, use the Trapezoidal Rule with to find the rate of the volume of flow of water in the river. Hint: Volume of flow = rate of flow area of cross section.

The present value of a perpetual stream of income that flows continually at the rate of dollars per year is given by the formula where is the interest rate compounded continuously.Using this formula, find the present value of a perpetual net income stream that is generated at the rate of dollars per year. Hint: .

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

Find the indefinite integral.

Use the table of integrals to find the integral.

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

The life span (in years) of a certain brand of color television tube is a continuous random variable with probability density function How long is one of these color television tubes expected to last? __________ year(s)

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.

Find the indefinite integral. Hint: First, make the substitution ; then, integrate by parts.

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

The average waiting time for patients arriving at the Newtown Health Clinic between 1 P.M.and 4 P.M.on a weekday is an exponentially distributed random variable x with expected value of 30 minutes. What is the probability that a patient arriving at the clinic between 1 P.M.and 4 P.M.will have to wait between 27 and 32 minutes? Round your answer to two decimal places.

Cooper Realty is considering development of a time-sharing condominium resort complex along the oceanfront property illustrated in the accompanying graph.To obtain an estimate of the area of this property, measurements of the distances from the edge of a straight road, which defines one boundary of the property, to the corresponding points On the shoreline are made at 100-ft intervals.Using simpson's Rule with n = 10,estimate the Area of oceanfront property.

Find the indefinite integral.

The amount of time t (in seconds) it takes a motorist to react to a road emergency is a continuous random variable with probability density function What is the expected reaction time for a motorist chosen at random?

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

Find the indefinite integral. Hint: First, make the substitution ; then, integrate by parts.

The life span (in years) of a certain brand of color television tube is a continuous random variable with probability density function How long is one of these color television tubes expected to last?

In using the trapezoidal rule, the number of subintervals n must be even.