1. Antiderivatives
5.1

2. Discovery of Power Rule for Antiderivatives
If f ‘ (x) =
Then f(x) =
If f ‘ (x) =
Then f(x) =
If f ‘ (x) =
Then f(x) =
If f ‘ (x) =
Then f(x) =

4. Tells us the variable of integration
Differentiation
Integration
The process of finding a derivative
The process of finding the antiderivative
Tells us the variable of integration
Symbols:
Integral
Symbols:
Integrand

5. The antiderivatives vary by a constant!
is the indefinite integral of f(x) with respect to x.
Each function has more than one antiderivative (actually infinitely many)
Derivative of:
The antiderivatives vary by a constant!

6. General Solution for an Indefinite Integral
You will lose points if you forget dx or + C!!!
Where c is a constant

7. Basic Integration Formulas

8. You can always check your answer by differentiating!
Find:
You can always check your answer by differentiating!

9. Basic Integration Rules

10. C represents any constant
Evaluate:
C represents any constant

11. Evaluate:

12. Evaluate:

13. Evaluate:

14. Evaluate:

15. Particular Solutions
and F(1) = 0