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Approximate Integration- Trapezoidal and Simpson's Rule

Approximate Integration- Trapezoidal and Simpson's Rule

In order to evaluate 10aint1 , the interval [a,b] is subdivided into n subintervals

each of length:

10aint2

x0 = a
x1 = a + h
x2= a + 2h
x3 = a + 3h

xi = a + ih
xn = a + nh = b

Then find the corresponding y = f(x) and use one of the following:

Trapezoidal Rule:

Value of Area; AT = h / 2 (y0 + 2y1 + 2y2 + . . . + 2yn-1 + yn)

Error; ET = -( h2 / 12 ) (b - a) f '' (c); where a £ c £ b.

Simpson's Rule:

Value of area; As= h / 3 ( y0 + 4y1 + 2y2 + 4y3 + 2y4 + . . . + 2yn-2 + 4yn-1 + yn )

Error; Es = - (h4 / 180) ( b - a) f(4)(c); where a £ c £ b.

 

Subject: 
Calculus
Subject X2: 
Calculus

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