Exam 5: Integrals

Alabama Instruments Company has set up a production line to manufacture a new calculator.The rate of production of these calculators after weeks is calculators per week.Production approaches 5,700 per week as time goes on, but the initial production is lower because of the workers' unfamiliarity with the new techniques.Find the number of calculators produced from the beginning of the third week to the end of the fourth week.Round theAnswer to the nearest integer.

Evaluate the Riemann sum for with four subintervals, taking the sample points to be right endpoints.Select the correct Answer

Find the derivative of the function.

Select the correct Answer for each question. -The velocity of a car was read from its speedometer at ten-second intervals and recorded in the table.Use the Midpoint Rule to estimate the distance traveled by the car.

Evaluate the definite integral.

Determine a region whose area is equal to

Evaluate the integral by interpreting it in terms of areas.

Evaluate the integral.

Evaluate the integral.

The velocity graph of a braking car is shown.Use it to estimate to the nearest foot the distance traveled by the car while the brakes are applied.Use a left sum with

Find the indefinite integral.

Evaluate the indefinite integral.

Find the integral.

The speed of a runner increased steadily during the first three seconds of a race.Her speed at half-second intervals is given in the table.Find a lower estimate for the distance that she traveled during these three seconds.

Select the correct Answer for each question. -Find the area of the region under the graph of on [

Find the integral using an appropriate trigonometric substitution.

Evaluate the limit by interpreting it as the limit of a Riemann sum of a function on the interval [a, b].

Use the definition of area to find the area of the region under the graph of on [ using the indicated choice of [0, 6], is the left endpoint

Express the limit as a definite integral on the given interval.

Select the correct Answer: for each question. -Find the integral using an appropriate trigonometric substitution.