Exam 7: Additional Topics in Integration

Suppose the time intervals between arrivals of successive cars at an expressway tollbooth during rush hour are exponentially distributed and that the average time interval between arrivals is 8 seconds. Find the probability that the average time interval between arrivals of successive cars is more than 17 seconds. Round your answer to two decimal places.

Use the formula to find the integral.

Find the function f given that the slope of the tangent line to the graph of f at any point and that the graph passes through the point (0, 7).

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.

Determine the value of the constant k so that the function is a probability density function on the interval .

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

Find the expected value of the continuous random variable X associated with the probability density function over the indicated interval.

Use the table of integrals to find the integral.

Determine the value of the constant k so that the function is a probability density function on the 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. Find the exact value of the integral. Please give the answer to four decimal places.

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

Use the table of integrals to find the integral.

Evaluate the following improper integral whenever it is convergent.

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

The number of voters in a certain district of a city is expected to grow at the rate of people per year years from now. If the number of voters at present is , how many voters will be in the district years from now?

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

Evaluate the definite integral by using the method of integration 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?

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.