1. Antiderivatives

2. Indefinite Integral The family of antiderivatives of a function f indicated by The symbol is a stylized S to indicate summation 2

3. Indefinite Integral The indefinite integral is a family of functions The + C represents an arbitrary constant The constant of integration 3

4. Properties of Indefinite Integrals The power rule The integral of a sum (difference) is the sum (difference) of the integrals 4

5. Properties of Indefinite Integrals The derivative of the indefinite integral is the original function A constant can be factored out of the integral 5

6. Example : Evaluate

7. Examples Determine the indefinite integrals as specified below 7

8. Integrate

9. Find each antiderivative

13. Solve the differential equation

17. Given that the graph of f(x) passes through the point (1,6) and that the slope of its tangent line at (x.f(x) is 2x+1, find f(6)