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Midpoint and Trapezoidal Rules. Approximating Integrals. There are some cases when it is impossible to find the definite integral They can be approximated by using types of Riemann sums. Midpoint Rule. Midpoints of drawn rectangles are used where . Trapezoidal Rule. - PowerPoint PPT Presentation
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Midpoint and Trapezoidal Rules
There are some cases when it is impossible to find the definite integral
They can be approximated by using types of Riemann sums
Approximating Integrals
Midpoints of drawn rectangles are used
where
Midpoint Rule
1 2( ) ( ) ( )... ( )b
naf x dx x f x f x f x
b axn
Uses trapezoids instead of rectangles
Trapezoidal Rule
0 1 2( ) ( ) 2 ( ) 2 ( ) ..... ( )2
b
na
xf x dx f x f x f x f x
Use both the Midpoint and Trapezoidal rules to evaluate the integral with n = 5
Example
2
1
1 dxx
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