Chapter 7 Integration.

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Presentation transcript:

Chapter 7 Integration

Section 7.1 Antiderivatives

Figure 1

Your Turn 2 Solution:

Your Turn 3 Solution: By extending the sum and difference rules to more than two terms, we get

Your Turn 4 Solution: First rewrite the integrand as follows.

Your Turn 5 Solution:

Section 7.2 Substitution

Your Turn 1 Solution: Now substitute. Now replace u with

Your Turn 2 Solution:

Your Turn 4 Solution:

Area and the Definite Integral Section 7.3 Area and the Definite Integral

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

The Fundamental Theorem of Calculus Section 7.4 The Fundamental Theorem of Calculus

Your Turn 1 Solution: By the power rule given earlier, the indefinite integral is By the Fundamental Theorem, the value of the definite integral is found by evaluating as follows with no constant C required.

Your Turn 2 Solution: Use the Fundamental Theorem.

Figure 18

Figure 19

Figure 20

The Area Between Two Curves Section 7.5 The Area Between Two Curves

Figure 21

Figure 22

Figure 23

Figure 25

Figure 26

Figure 27

Figure 28

Figure 29

Figure 30