18 Numerical_Integration

# 18 Numerical_Integration - 18 Numerical Integration...

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18 - Integration - 1 18 - Numerical Integration Remember that integrating a function falls under two categories: Definite and Indefinite Integrals. A definite integral is defined as = b a dx x f A ) ( while an indefinite integral is defined as + = C d f t g τ τ ) ( ) ( Now, in the computer, it’s a fairly straightforward task to compute a definite integral. All we need to do is to compute the area under the function. To find the area between two nearby points, x ( j ) and x ( j +1), it is necessary to compute the area under the curve segment defined below Trapezoidal Rule How do we compute the area? It really depends on how we want to approximate the value of the function between x j and x j+1 . We could use the beginning value, y j , and compute the area of a rectangle j j j x x y x x A j j ) ( 1 , 1 = + + Alternatively, we could use the ending value x y x j+1 x y y

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18 - Integration - 2 1 1 , ) ( 1 + + = + j j j x x y x x A j j or, we could use some average value between y j and y j+1 . The trapezoidal rule for
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