1. Integration By Jason Leitmeyer, Shannon Hunt, Doris Bittner

2. Outline Indefinite Integrals Definite Integrals Using Integration to Find Area ◦ Total Area ◦ Net Signed Area Rectilinear Motion Using Integration ◦ Position, Velocity, Speed, Acceleration

3. Indefinite Integrals Integral Power Rule A constant factor can be moved through an integral sign

4. Indefinite Integrals (cont.) Examples 1) 2)

5. Indefinite Integrals (cont.) 3) 4) 5)

6. Definite Integrals

7. Definite Integrals (cont.)

8. Rectilinear Motion using integration Find the position function for a particle v(0)=0 s(0)=0

9. Rectilinear Motion Signed Area – plug into calculator Total Area- Plug into calculator Find the total area between the curve Y=sinx and the x- axis over the interval [0,2 π ]

10. Computing Displacement and Velocity by Integration

11. Computing Displacement and Velocity by Integration (cont.) Find the position, velocity, speed and acceleration at time t= π if v(t)=cos(t) s(0)=1

12. Computing Displacement and Velocity by Integration (cont.) Find the position function for a particle v(0)=0 s(0)=0