Integration Techniques: Tables OBJECTIVE Evaluate integrals using a table of integration formulas. Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables TABLE 1: Integration Formulas Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables TABLE 1 (continued): Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables TABLE 1 (continued): p. 453, formula 12, there is no “+C” Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables TABLE 1 (continued): Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables TABLE 1 (continued): Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables TABLE 1 (concluded): Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Example 1: Evaluate: This integral fits formula 20 in Table 1. Here, a = –1 and b = 3. So, we have Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Quick Check 1 Evaluate: This integral fits formula 19 in Table 1. Here, Note that there is a coeficient of 2 that we need to take into account. So we have, Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Example 2: Evaluate: First, factor the 5 out of the integral. Then, this integral fits formula 18 in Table 1. Here, a = 7 and b = –8. So, we have Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Quick Check 2 Evaluate: This integral fits formula 21 in Table 1. Here, Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Example 3: Evaluate: This integral almost fits formula 22 in Table 1; but the coefficient of x2 needs to be 1. To achieve this, first factor out the 16. Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Example 3 (continued): Now, and by formula 22, Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Example 4: Evaluate: This integral fits formula 14 in Table 1. Here, a2 = 25, so a = 5. Thus, we have Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Quick Check 3 Evaluate: This integral fits formula 14 in Table 1. Here, So we have, Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Example 5: Evaluate: This integral fits formula 9 in Table 1. We must, however, apply the formula 3 times. Copyright © 2014 Pearson Education, Inc.

4.7 Integration Techniques: Tables Section Summary Tables of integrals or the Web site www.integrals.com can be used to evaluate many integrals. Some algebraic simplifications of the integrand may be required before the correct integral form can be identified. Copyright © 2014 Pearson Education, Inc.