1. 5.1 Integrals
Rita Korsunsky

2. Definition A function F is an antiderivative of f on an interval I if for every x in I
……………

3. Indefinite integral
because

4. y
When C = 0
C = -1 2
C = 1
C = -2 1 x
C = 2 -1 -2

6. Examples

7. Theorem
Proof:

8. Properties of the Integral
for any constant c
Proof:

9. Example
Evaluate

10. Evaluate
Example

11. Example
Evaluate

12. Example
Find the equation of the curve that passes through (1,-1) and whose slope at any point (x,y) is 3x 2
Step One – Integrate
Step Two - Substitute initial conditions
Step Three - Solve for C
Step Four - Substitute C back into general solution equation

13. THE END