Exam 7: Additional Topics in Integration

Nine milligrams of a dye (D) are injected into a vein leading to an individual's heart. The concentration of the dye in the aorta measured at 2-second intervals is shown in the accompanying table. Use Simpson's rule and the formula to estimate the person's cardiac output. Round the result to the nearest tenth. __________ L/min

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

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

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.

Use the table of integrals to find the integral.

Find the indefinite integral.

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

Find the indefinite integral.

Evaluate the definite integral by using the method of integration by parts.

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

Find the indefinite integral.

Determine whether the statement is true or false. If is a probability density function of a continuous random variable in the interval , then the expected value of is given by

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

Find the indefinite integral.

Determine whether the statement is true or false. If is a probability density function of a continuous random variable in the interval , then the expected value of is given by

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

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 for 95 days or less. Please round the answer to the nearest thousandth if necessary. __________ Find the probability that a plant of this species will live more than 130 days. Please round the answer to the nearest thousandth if necessary. __________ Find the probability that a plant of this species will live more than 60 days but less than 150 days. Please round the answer to the nearest thousandth if necessary. __________

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

Evaluate the following improper integral whenever it is convergent.

Determine whether the statement is true or false. Simpson's rule is less accurate than the trapezoidal rule.