# Practice Problems

## Practice Problems

(a) Use part 2 of the Fundamental Theorem to find a formula for and then differentiate to obtain a formula for . Evaluate at and .

(b) Use part 1 of the Fundamental Theorem to evaluate at and .

In problems 3 – 7 , evaluate at and .

In problems 9 – 11 for the functions in Figures 10 – 14. Evaluate .

In problems 13 – 33, verify that is an antiderivative of the integrand and use Part 2 of the Fundamental Theorem to evaluate the definite integrals.

For problems 33 – 47, find an antiderivative of the integrand and use Part 2 of the Fundamental Theorem to evaluate the definite integral.

In problems 49 – 53 , find the area of each shaded region.

49. Region in Fig. 14.

51. Region in Fig. 16.

53. Region in Fig. 18.

**Leibniz' Rule**

Source: Dale Hoffman, https://learn.saylor.org/pluginfile.php/1403575/mod_resource/content/2/CC_4_5_FundamentalThm.pdf

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