# Practice Problems

## Practice Problems

In problems 1 – 3 , rewrite the limit of each Riemann sum as a definite integral.

In problems 5 – 9, represent the area of each bounded region as a definite integral. (Do **not** evaluate the integral, just translate the area into an integral.)

5. The region bounded by , the x–axis, the line , and .

7.The region bounded by , the x–axis, the line , and .

9. The shaded region in Fig. 10.

In problems 11 – 15 , represent the area of each bounded region as a definite integral, and use geometry to determine the value of the definite integral.

11. The region bounded by the x–axis, the line , and .

13. The region bounded by , the x–axis, and the line .

15. The shaded region in Fig. 12.

17. Fig. 14 shows the graph of and the areas of several regions.

Evaluate:

In problem 19 , your velocity (in feet per minute) along a straight path is shown. (a) Sketch the graph of your location. (b) How many feet did you walk in 8 minutes? (c) Where, relative to your starting location, are you after 8 minutes?

19. Your velocity is shown in Fig. 16.

In problems 21 – 27, the units are given for and . Give the units of .

21. is time in "seconds", and is velocity in "meters per second".

23. is a position in "feet", and is an area in "square feet".

25. is a height in "meters", and is a force in "grams".

27. is a time in "seconds", and is an acceleration in "feet per second per second .

29. For , partition the interval [0,2] into n equally wide subintervals of length . Write the lower sum for this function and partition, and calculate the limit of the lower sum as . (b) Write the upper sum for this function and partition and find the limit of the upper sum as .

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-5.3-Definite-Integral.pdf

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