1. Indefinite Integrals

2. Objectives Students will be able to Calculate an indefinite integral. Calculate a definite integral.

3. Definition The symbol ∫is the integral sign; f(x) is the integrand; x is the variable of integration; and C is the constant of integration.

4. Important Integrals

5. General Rules of Integration where a is a constant

6. Example 1 Evaluate the indefinite integral

7. Example 2 Evaluate the indefinite integral

8. Example 3 Evaluate the indefinite integral

9. Example 4 Evaluate the indefinite integral

10. Example 5 Evaluate the indefinite integral

11. Example 6 Evaluate the indefinite integral

12. Example 7 Evaluate the indefinite integral

13. Example 8 Under certain conditions, the number of diseased cells N(t) at time t increases at a rate where A is the rate of increase at time 0 (in cells per day) and k is a constant. a.Suppose A = 60, and at 4 days, the cells are growing at a rate of 300 per day. Find a formula for the number of cells after t days, given that 400 cells are present at t = 0. b.Use your answer from part a to find the number of cells present after 11 days.

14. Example 9 Suppose v(0)= –7, and s(0) = 12. Find s(t).