# Practice Problems

## Practice Problems

Problems 1 – 19 refer to the graph of f in Fig. 13. Use the graph to determine the values of the definite integrals. (The bold numbers represent the area of each region.)

Problems 21 – 29 refer to the graph of g in Fig. 14. Use the graph to evaluate the integrals.

For problems 31 – 33, use the constant functions and on the interval [0,2]. Calculate each integral and verify that the value obtained in part (a) is not equal to the value in part (b).

31. (a) (b) \int_{0}^{2} \mathrm{f}(x) \cdot \mathrm{g}(x) \mathrm{dx}\)

For problems 35 – 41, sketch the graph of the integrand function and use it to help evaluate the integral.

For problems 43 – 45, (a) Sketch the graph of and (b) sketch the graph of .

For problems 47 – 49, state whether the function is (a) continuous on [1,4], (b) differentiable on [1,4] , and (c) integrable on [1,4].

51. Write the total distance traveled by the car in Fig. 19 between 1 pm and 4 pm as a definite integral and estimate the value of the integral.

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-5.4-Properties-of-the-Definite-Integral.pdf

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