1. Warm Up

2. 7.1 A – Initial Value Problems

3. Consider: then: or It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears. However, when we try to reverse the operation: Given: find We don’t know what the constant is, so we put “C” in the answer to remind us that there might have been a constant. Think about it….

4. Integrals such as are called definite integrals because we can find a definite value for the answer. The constant always cancels when finding a definite integral, so we leave it out! So far, we have found definite integrals.

5. Integrals such as are called indefinite integrals because we can not find a definite value for the answer. When finding indefinite integrals, we always include the “plus C”. Indefinite Integrals

6. Common antiderivatives YOU NEED TO KNOW

7. More...

8. Examples

9. More Examples

10. Initial Value Problems We cannot find C unless additional information is given. All we need is a single point, called an initial condition. A problem with an initial condition is called a initial value problem.

11. Example

12. Find the position function for v(t) = t 3 - 2t 2 + t s(0) = 1 C = 1

13. Homework