Trapezoidal Rule of Integration: Example

Learn the trapezoidal rule of integration through a simple example.

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Education

Tags:

• Trapezoidal
• Rule
• Example
• Numerical
• Integration
• Methods
• numerical
• methods
• numericalmethodsguy

[YoZZgAtLiii66]

can i also geht the true error by using richardson extrapolation for romberg integration?

[numericalmethodsguy]

@YoZZgAtLiii66 No, because richardson's extrapolation method is just that - extrapolation, not a true value. You can get an estimate of the true error though.

[Hyunikil]

thanks , but @ 06:53 the error is only the area above the rectangle ? what about the small areas on the sides ? are they included in the true error or not ?

[numericalmethodsguy]

@Hyunikil The error in this case is the difference between the area under the curve from lower limit of integration to upper limit of integration and the area of the trapezoid!

[Hyunikil]

@numericalmethodsguy in this case if i took my lower limit and upper limit two close values i.e 0.1 and 0.2 , how it will effect my error value ? will it become less or more accurate ? 

[numericalmethodsguy]

@Hyunikil Well you can calculate it and see if it is less or more. Of course, the true error in Trapezoidal rule is produict of the value of second derivative of the function at some point between 'a' and 'b', and 1/12*(b-a)^3. Go to numericalmethods(dot)eng(dot)u­sf(dot)edu, click on Search>Keyword, click on Trapezoidal rule, click on pdf of the textbook chapter and look at page 14.

[Hyunikil]

@numericalmethodsguy ok thanks for your time

[ahmadk19]

thank you!! please keep posting your tutorials, they help out a lot. Can you do golden section and Fibonacci search methods as well?