Lec18 - Lecture 18 Integration Analytical Basic functions...

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Lecture 18 Numerical Integration 1 Lecture 18 Integration Analytical Basic functions polynomial trigonometric natural logarithm Numerical trapezoid method a polynomial example solar flux example
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Lecture 18 Numerical Integration 2 Analytical integrals of simple functions. 1 to equal not n for - - + + - = + + = + + + + ) ( 1 ) ( 1 ) ( 1 1 1 | | i f n i n f x x x x n x x n x x c n x x a cx n ax dx c ax f i f i f i ) cos( ) cos( ) cos( ) sin( f i x x x x x x x dx x f i f i - = - = ) sin( ) sin( ) sin( ) cos( i f x x x x x x x dx x f i f i - = = i f f i f i x x x x x x x x e e e dx e - = = ) ln( ) ln( ) ln( 1 i f x x x x x x x dx x f i f i - = =
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Lecture 18 Numerical Integration 3 -5 -4 -3 -2 -1 0 1 2 3 4 5 -3 -1 1 3 5 f(x) x f(x) = -0.3x 2 + x + 2 Definition of a definite integral The integral of f(x) from x = -1 to 3.5 is equal to the shaded area under the curve.
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Lecture 18 Numerical Integration 4 Integral of our example function = + + - - dx x x ) 2 3 . 0 ( 5 . 3 0 . 1 2 = + + - - - - | | | 5 . 3 0 . 1 5 . 3 0 . 1 2 5 . 3 0 . 1 3 2 2 3 3 . 0
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This note was uploaded on 02/26/2008 for the course ENGR 1 taught by Professor X during the Spring '07 term at Lehigh University .

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Lec18 - Lecture 18 Integration Analytical Basic functions...

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