Exam 7: Additional Topics in Integration

Find a bound on the error in approximating the given definite integral using the trapezoidal rule with n intervals. If necessary, round the answer to three decimal places. Find a bound on the error in approximating the given definite integral using the Simpson's rule with n intervals. If necessary, round the answer to five decimal places.

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

Use the table of integrals to find the integral.

In a submerged trial run of an attack submarine, a reading of the sub's velocity was made every quarter hour, as shown in the accompanying table.Use the trapezoidal rule to estimate the distance traveled by the submarine during the 2-hour period.Please round the answer to the nearest hundredth if necessary. __________ miles

The management of AstroWorld ("The Amusement Park of the Future") estimates that the number of visitors (in thousands) entering the amusement park t hours after opening time at 10 am is given by per hour.Determine the number of visitors admitted by noon.

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

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

Find the indefinite integral.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places. Trapezoidal rule:__________ Simpson's rule: __________ Exact value: __________

The demand function for Apex women's boots is where p is the wholesale unit price in dollars and x is the quantity demanded daily, in units of a hundred.Find the consumers' surplus if the wholesale price is set at $70/pair.Round the result to the nearest dollar. $__________

As a result of increasingly stiff laws aimed at reducing the number of alcohol-related traffic accidents in a certain state, preliminary data indicate that the number of such accidents has been changing at the rate of accidents/month t months after the laws took effect.There were 912 alcohol-related accidents for the year before the enactment of the laws.Determine how many alcohol-related accidents were expected during the first year the laws were in effect.Please round the answer to the nearest integer. __________ accidents

Determine whether the statement is true. If exists, then exists and . Answer yes or no.

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 13% / year compounded continuously, find the accumulated value of this stream of income at the end of 8 years .Round to the nearest dollar.

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).

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

The number of chocolate chips in each cookie of a certain brand has a distribution described by the probability density function Find the expected number of chips in each cookie.

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure.The measurements shown were taken at 10-ft intervals.Using Simpson's rule with , estimate the surface area of the lake.Round the result to the nearest tenth.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral.Compare your result with the exact value of the integral.Please give the answer to four decimal places. Trapezoidal rule: __________ Simpson's rule: __________ Exact value: __________