Exam 5: Accumulated Change: the Definite Integral

The upper half of the ellipse below has equation . Find the area in the first quadrant between the ellipse and the line . Give your answer to two decimal places.

After a foreign substance is introduced into the blood, the rate at which antibodies are made is given by thousands of antibodies per minute, where time t is measured in minutes and . If there are no antibodies in the blood at t = 0, how many antibodies are there after 5 minutes? Round to the nearest whole number.

The flow rate of water in a mountain stream due to spring runoff is given in the following table. Give your best estimate (average of upper and lower limit) of how many cubic meters of water flowed through from 6:00 pm to midnight.

The following table gives the rate , in cubic centimeters, that air is leaking from a balloon t seconds after it is inflated. Estimate .

At time t, in seconds, your velocity, v, in meters per second, is given by for . Use to estimate how many meters you traveled during this time.

The rate of growth of the net worth of a company is given by dollars per year t years after its formation in 1990. How much did it increase in value between 1990 and 2005?

The graph below shows a marginal cost function, $ per item. If the fixed cost is $900, estimate the total cost of producing 250 items.

The following figure shows the rate of growth of two cities, with being the growth of City A after t years and being the growth of City B after t years. If the two cities have the same population at t = 0, arrange the following values in order from smallest to largest by placing a "1" by the smallest, a "2" by the next smallest, and so forth. A. B. C. D.

The rate of pollution pouring into a lake is measured every 10 days, with results in the following table. About how many tons of pollution have entered the lake during the first 40 days?

Suppose is given by the following graph. If , what is ?

Using the following figure, calculate the value of the right-hand Riemann sum for the function f on the interval using .

Use a calculator to evaluate . Round your answer to 2 decimal places.

The following figure shows the graph of the velocity, v, of an object (in meters/sec). If the graph were shifted up 4 units, how would the distance traveled between t = 0 and t = 6 change?

Use the following figure to find the value of

If and f is continuous, then f must have at least one zero between a and b (assume ).

Consider a sports car which accelerates from 0 ft/sec to 85 ft/sec in 5 seconds (85 ft/sec = 58 mph). The car's velocity is given in the following table. What is the lower bound for the number of feet the car travels in 5 seconds?

The graph below shows the velocity of an object (in meters/second). Find an upper bound for the number of meters traveled from t = 1 to t = 5 seconds.

The marginal cost function of producing a particular product is given by , where q is the number of items produced. If the fixed costs are $4000 and the items are sold for $700 each, what is the break even point?

Consider the graph of the function shown in the following figure. A. Approximate by using a right-hand sum with 3 subdivisions. Round to 2 decimal places. B. Is your answer to part (A) a lower or an upper estimate?

The following figure shows the rate of change of enrollment for a community college. Estimate the total change in enrollment over the first 6 years.