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Integration

Integration

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Integration

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  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 [0,2π]

  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