Trapezoidal Rule of Integration

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What is Integration

b

a

dx)x(fI

Integration:

The process of measuring

the area under a function

plotted on a graph.

Where:

f(x)

is the integrand

a= lower limit of integration

b= upper limit of integration

f(x)

a

b

b

a

dx)x(f

y

x

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Basis of Trapezoidal Rule

b

a

dx)x(fI

)x(f)x(f n

Trapezoidal Rule is based on the Newton-Cotes Formula

that states if one can approximate the integrand as an nth

order polynomial…

where

n

n

n

nn xaxa...xaa)x(f

1

110

and

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Basis of Trapezoidal Rule

b

a

n

b

a

)x(f)x(f

Then the integral of that function is approximated by

the integral of that nth order polynomial.

Trapezoidal Rule assumes n=1, that is, the area

under the linear polynomial,

2

)b(f)a(f

)ab(

b

a

dx)x(f

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##### Document information

Uploaded by:
pankarithi

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University:
Ankit Institute of Technology and Science

Subject:
Numerical Methods

Upload date:
17/04/2013