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Quiz #1 30/30 congratulations 1)AL-AMER, AHMAD ADNAN MOHA 2)AL-AGEELI, AHMAD IBRAHIM 3)AL-GARNI, BANDAR HASSAN S 4)AL-ARJANI, ALI SAEED ABDU 5)AL-BUGMI, TURKI MAHDI SHA 6)AL-BARAK, MUHAMMAD ABDUL 7)AL-MARRI, ALI MUHAMMAD FA 8)AL-HASAN, KHALED MUHAMMAD 9)AL-MANSOUR, ABDUL-RHMAN M 10)MAKKI, EMAD AHMAD MUHAMMA 11)AL-MESHAL, SAMI MUHAMMAD
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2) an indefinite integral MATLAB can find 1) a definite integral syms x Int(x^2, x, 0, 1) syms x Int(x^2, x)
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Group # 1 Turki al bogmi Turad al hujile Ahmad aquile Emad Makki Groups
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Problem 1
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9.9 Line Integral Independent of the Path Evaluate.along the curve C between (-3,-3) and (3,3) (-3,-3) (3,3)
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Problem 2
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9.9 Line Integral Independent of the Path Evaluate.along the curve C between (-3,-3) and (3,3) (-3,-3) (3,3)
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Problem 3
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9.9 Line Integral Independent of the Path Evaluate.along the curve C between (-3,-3) and (3,3) (-3,-3) (3,3)
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The Integral has the same value The integral Is independent of the path (-3,-3) (3,3 ) (-3,-3) (3,3) (-3,- 3) (3,3)
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Under what condition the integral is independent of the path is an exact differential
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Test for exact differential is an exact differential
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Problem 4
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Which line integral is dependent of the path A) C) B) Example3 Example4 HW 7
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Problem 5
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Application (1) Evaluate.along the curve C between (-3,-3) and (4,4) (4,4) (-3,-3) (4,0) (0,-3)
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Problem 6
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Evaluate Application (2) (4,4) (-3,-3) (4,0) (0,-3).along the curve C between (-3,-3) and (4,4)
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Exact differential is an exact differential There exists a function Such that Example
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Theorem 9.8 Fundamental Theorem for Line Integral Suppose there exists a function such that ;that is, is an exact differential. Then depends on only the endpoints A and B of the path C and
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Application (1) Evaluate.along the curve C between (-3,-3) and (4,4) (4,4) (-3,-3) (4,0) (0,-3)
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How to find Method 2 Method 1 Which method ????? Easy step 1
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(-1,0) (3,4)
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Notation If Is independent of the path between the endpoints A and B, then we write
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Theorem 9.10 Test for Path Independence Is independent of the path
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How to find
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Conservative Vector Fields If the Is independent of the path, then 2) F is said to be a gradient field 3) F is said to be conservative 4) Is a potential function for F
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Conservative Vector Fields In a gradient force field F, 1)The work done by the force upon a particle moving from position A to position B is the same for all paths. 2)The work done by a force along a closed path is zero In a conservative field F, 1)The law of conservation of mechanical energy holds. 2)For a particale moving along a path in a conservative field, kinetic energy + potential energy = constant WHY????
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Is independent of the path 9.9 9.7 Conservative Vector Fields
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Remarks (pp501) A frictional force such as air resistance is neoconservative. Neoconservative forces are dissipative in that their action reduces kinetic energy without a corresponding increase in potential energy. In other words, if the work done depends on the path, then F is neoconservative.
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9.9 Homework
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(2,0) (-2,0)
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9.9 Homework
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