Learning Outcomes

1. Find the general antiderivative of a given function.
2. Explain the terms and notation used for an indefinite integral.
3. Use anti differentiation to solve simple initial-value problems.

Textbook

• Chapter 4.10  Antiderivatives

Textbook Assignment

• p. 497:    465, 468-471 all, 473, 476, 477, 481, 482, 490-493 all, 499, 500, 502

WeBWork Assignment

• Application-Antiderivatives

Exit problems of the session

1. Evaluate following indefinite integrals:

(a). (b). (c). (d). 2. Solve the initial value problem: , .

Key Concepts

• If for all in the domain of ,  then is an antiderivative of .
• The most general antiderivative of is the indefinite integral of , denoted by the notation .  If is an antiderivative of ,  then , is any constant

• Properties of indefinite integrals: Let and be antiderivatives of and , respectively and let be any real number, then  • Basic indefinite integral formulas: ;   ;  ;  ; ; ; ; ; ;

• Solve the initial-value problem , requires us first find the set of antiderivatives of and then to look for the particular antiderivative that also satisfies the initial condition, that is to use initial condition to find integral constant #### Videos and Practice Problems of Selected Topics

1. Antiderivatives and indefinite integrals (3:42) What is the antiderivative of ?
2. * Practice: antiderivatives and indefinite integrals (4 problems)
3. Reverse power rule (5:47) Deriving followed by finding and .
4. * Practice: Reverse power rule. (4 problems)
5. * Practice: Reverse power rule with negative and fractional powers. (4 problems)
6. Indefinite integrals: sums and multiples (4:55) The indefinite integral of a sum and a multiple of a function. Find and .
7. * Practice: Reverse power rule with sums and multiples. (4 problems)
8. Rewriting before integration (5:16) Find , , .
9. * Practice: Reverse power rule: rewriting before integrating. (4 problems)
10. Indefinite integrals of , and (4:03) Find and .
11. * Practice: Indefinite integrals: and . (4 problems)
12. * Practice: Indefinite integrals: and . (4 problems)