1. Integration Techniques: Tables
OBJECTIVE
Evaluate integrals using a table of integration formulas.
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2. 4.7 Integration Techniques: Tables
TABLE 1: Integration Formulas
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3. 4.7 Integration Techniques: Tables
TABLE 1 (continued):
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4. 4.7 Integration Techniques: Tables
TABLE 1 (continued):
p. 453, formula 12, there is no “+C”
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5. 4.7 Integration Techniques: Tables
TABLE 1 (continued):
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6. 4.7 Integration Techniques: Tables
TABLE 1 (continued):
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7. 4.7 Integration Techniques: Tables
TABLE 1 (concluded):
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8. 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
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9. 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,
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10. 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
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11. 4.7 Integration Techniques: Tables
Quick Check 2
Evaluate:
This integral fits formula 21 in Table 1.
Here,
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12. 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.
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13. 4.7 Integration Techniques: Tables
Example 3 (continued):
Now, and by formula 22,
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14. 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
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15. 4.7 Integration Techniques: Tables
Quick Check 3
Evaluate:
This integral fits formula 14 in Table 1.
Here, So we have,
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16. 4.7 Integration Techniques: Tables
Example 5: Evaluate:
This integral fits formula 9 in Table 1.
We must, however, apply the formula 3 times.
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17. 4.7 Integration Techniques: Tables
Section Summary
Tables of integrals or the Web site can be used to evaluate many integrals.
Some algebraic simplifications of the integrand may be required before the correct integral form can be identified.
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