Trapezoidal Rule of Integration - Numerical Methods - Lecture Slides, Slides for Numerical Methods. Ankit Institute of Technology and Science

Numerical Methods

Description: The main points are: Trapezoidal Rule of Integration, Process of Measuring Area, Lower Limit of Integration, Basis of Trapezoidal Rule, Newton-Cotes Formula, Linear Polynomial, Derivation of Trapezoidal Rule, Area of Trapezoid
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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
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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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