SECTION 4-1 Antidifferentiation Indefinite Integration

differentiation antidifferentiation

1) If y = x 3 find y’ by the power rule: 2) Given y’ = 3x 2 find y think backwards:

3) Given find y Is that the only function? What about… y = x 2 – 5 OR y = x 2 + 3

Antiderivatives Def: Antiderivatives Vary by any number C where C is called the constant of integration The equation itself is the general solution that represents the family of solutions obtained by finding the antiderivative.

Indefinite Integration: the process of finding antiderivatives Notation: Integral Sign Integrand Variable of integration Antiderivative Constant of Integration

Basic Integration Rules (p. 243) Constants:(a) (b) (c) (d)

Basic Integration Rules Sum/Difference: Power:

4) 5)

6) 7)

Trig Integration Rules

8) 9)

Trig identities:

10)

11)

Homework Page 255 # 9-12, odd, 35, 36,37,40,and 44