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Integration By Jason Leitmeyer, Shannon Hunt, Doris Bittner.

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Presentation on theme: "Integration By Jason Leitmeyer, Shannon Hunt, Doris Bittner."— Presentation transcript:

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


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