Exam 7: Additional Topics in Integration

Evaluate the following improper integral whenever it is convergent.

Use the formula to find the integral.

Find the indefinite integral.

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

Becky Wilkinson wants to establish a trust fund that will provide her children and heirs with a perpetual annuity in the amount of thousand dollars per year beginning next year.If the trust fund will earn an interest rate of 10% per year compounded continuously, find the amount that she must place in the trust fund now. Hint: Use the formula .

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 800 hours of use? Round your answer to two decimal places. b. What is the probability that a robot will break down after 1,200 hours of use? Round your answer to two decimal places.

Use the formula to find the integral.

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 indefinite integral.

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

The life span of a certain plant species (in days) is described by the probability density function . Find the probability that a plant of this species will live more than 120 days.

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 .

Use the table of integrals to find the integral. Hint: First use the substitution u = x + 5.

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

Find the indefinite integral.

Find the indefinite integral.

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. $__________