1. Write the derivative for each of the following.

2. Calculus Indefinite Integrals Tuesday, December 15, 2015 (with a hint of the definite integral)

3. Each of the previous are Antiderivatives of f(x)=x 2 In mathematics notation: Integral sign integrand Variable Of Integration antiderivative Constant Of Integration

4. Recall the Slopefield concepts The slopefield of the differential equation y’ = x 2 has infinite solutions The slopefield of the differential equation y’ = x 2 has infinite solutions

5. We say the integral of f(x) with respect to x has as its antiderivative F(x) + C We say the integral of f(x) with respect to x has as its antiderivative F(x) + C Note that the antiderivative is the inverse of derivative just as integration is the inverse of differentiation Note that the antiderivative is the inverse of derivative just as integration is the inverse of differentiation

6. The indefinite integral vs. The definite integral

7. Note: The definite integral is a number. The definite integral is a number. The indefinite integral is a family of functions The indefinite integral is a family of functions

8. Integrate Reverse the derivative rule of a linear function

9. Reverse the power rule of differentation

10. Differentiation & Integration Rules Differentiation p. 173 Differentiation p. 173 Integration p. 180 Integration p. 180

11. Integrate

12. Rewrite integrals to fit the rules

13. Homework – Practice improves your understanding P. 181 1 – 10 P. 181 1 – 10 P. 182 31 – 41 odd P. 182 31 – 41 odd P. 186 51 – 59 odd P. 186 51 – 59 odd