Numerical Integration and Differentiation
EGN5455
Lecture 8

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Numerical Integration: Trapezoid rule
Objective: to approximate the integral on a
given interval [a,b].
Assumption: f(x) is a scalar-valued function of
x and has a continuous second derivative.
To find the linear polynomial which
interpolates (a,f(a)) and (b,f(b)), we can use
L
i
l
i
Lagrange interpolation:
b
a
x
b
f
b
b
x
a
f
)
)(
(
)
)(
(
a
a

Trapezoid rule
We integrate the Lagrange polynomial from a
to b, with the result:
).
(
)
(
)
(
2
1
a
b
b
f
a
f
Example1: Use the trapezoid rule to
approximate the integral of f(x)=x
2
on
interval [1,2].
5
.
2
1
2
)
2
(
)
1
(
2
/
1
f
f
The actual value is 7/3= 2.33

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