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Integration By Jason Leitmeyer, Shannon Hunt, Doris Bittner
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Outline Indefinite Integrals Definite Integrals Using Integration to Find Area ◦ Total Area ◦ Net Signed Area Rectilinear Motion Using Integration ◦ Position, Velocity, Speed, Acceleration
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Indefinite Integrals Integral Power Rule A constant factor can be moved through an integral sign
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Indefinite Integrals (cont.) Examples 1) 2)
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Indefinite Integrals (cont.) 3) 4) 5)
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Definite Integrals
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Definite Integrals (cont.)
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Rectilinear Motion using integration Find the position function for a particle v(0)=0 s(0)=0
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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 ]
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Computing Displacement and Velocity by Integration
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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
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Computing Displacement and Velocity by Integration (cont.) Find the position function for a particle v(0)=0 s(0)=0
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