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) , ( .......... ), , ( ), , ( ), , ( ; ) ( , int ) ( ; sin 2 2 1 1 n n o o y x y x y x y x table a of form the in given is x f or egration direct by calculated always not is dx x f dx x x n Integratio Numerical Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num. Meth. Dr.Adnan Jayed Zedan

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Page 1: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 2: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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curvetheunderareatheisdxxf

b

a

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 3: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 4: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 5: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 6: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 7: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 8: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 9: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 10: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 11: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 12: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 13: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 14: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 15: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 16: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 17: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 18: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 19: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 20: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 21: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 22: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 23: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 24: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 25: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 26: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

5

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 27: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 28: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 29: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 30: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 31: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 32: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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xf

Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 33: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 34: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan

Page 35: ³ ³ x by direct egration or f x is given in the Numerical ...ced.ceng.tu.edu.iq/images/lectures/Numerical-Methods/chapter7.pdf · int , ( ); ( ) sin x o y o x 1 y 1 x 2 y 2 x n

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Tikrit University-Civil Engineering Department Third Stage Eng.Anal.& Num.

Meth. Dr.Adnan Jayed Zedan