Exam 7: Additional Topics in Integration

Find the indefinite integral.

Find the area of the region bounded by the x-axis and the graph of the function

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

Find the indefinite integral.

a. Determine the value of the constant k so that the function is a probability density function on the interval . __________ b. If x is a continuous random variable with the probability density function given in part (a), find the probability that x will assume a value greater than 1. Round your answer to four decimal places.

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

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

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

The microprocessors, which are used in automobiles to regulate fuel consumption, are guaranteed against defects for 15,000 miles of use. Tests conducted in the laboratory under simulated driving conditions reveal that the distances driven before the microprocessors break down are exponentially distributed and that the average distance driven before the microprocessors fail is 80,000 miles. What is the probability that a microprocessor selected at random will fail during the warranty period? Please round the answer to the nearest hundredth.

Find the area of the region under the graph of from x = 1 to x = 9.