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# Ch4_8 - 1 Section 4.8 Numerical Integration Integration...

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Next Previous Chapter 4.8: Numerical Integration 11 ® Integration ® Analytical ® Basic functions l polynomial l trigonometric l natural logarithm ® Numerical ® trapezoid method ® a polynomial example ® solar flux example Section 4.8: Numerical Integration

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Next Previous Chapter 4.8: Numerical Integration 22 1 n all for ) x x ( c 1 n ) x x ( a cx 1 n ax dx ) c ax ( i f 1 n i 1 n f x x x x 1 n x x n | | f i f i f i - - + + - = + + = + + + + a ax ax a ax dx ax f i x x x x f i f i ) cos( ) cos( ) cos( ) sin( - = - = a ax ax a ax dx ax i f x x x x f i f i ) sin( ) sin( ) sin( ) cos( - = = a e e a e dx e i f f i f i ax ax x x ax x x ax - = = ) x ln( ) x ln( ) x ln( dx x 1 i f x x x x f i f i - = = Analytical integrals of simple functions
Next Previous Chapter 4.8: Numerical Integration 33 Definition of a definite integral -5 -4 -3 -2 -1 0 1 2 3 4 5 1 3 5 f(x) x f(x) = -0.3x2 + x + 2 The integral of f(x) from x = -1 to 3.5 is equal to the shaded area under the curve.

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Next Previous Chapter 4.8: Numerical Integration 44 dx ) 2 x x 3 . 0 ( 5 . 3 0 . 1 2 - + + - | | | 5 . 3 0 . 1 5 . 3 0 . 1 2 5 . 3 0 . 1 3 x 2 2 x 3 x 3 . 0 - - - + + - = )) 0 . 1 ( 5 . 3 ( 2 2 ) 0 . 1 ( 5 . 3 3 ) ) 0 . 1 ( 5 . 3 ( 3 . 0 2 2 3 3 - - + - - + - - - = 24 . 10 = Integral of our example function
Next Previous Chapter 4.8: Numerical Integration 55 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5

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Ch4_8 - 1 Section 4.8 Numerical Integration Integration...

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