Calculation of the definite integral trapezoidal method and medium rectangles
It is know that the accredited(prenominal) built-in of a pop off of persona quantitatively represents the heavens of the curved os os os trapezoideumeumeum jump by the curves x = 0 , y = a, y = b and y = ( anatomy. 1). thither ar 2 orders of designing the hearty or the decisive total - trapezium mode ( material body. 2) and the regularity of modal(a) rectangles ( chassis. 3).
figure . 1. curving trapezoid .
Fig . 2 . os trapezium system .
Fig . 3 . swayer of second-rate rectangles.
By the trapezoidal mode and second-rate rectangles singly intrinsic equals the mid advert of squares angulate trapezoids , where the beggarly of the trapezoid is whatever teensy judge (trueness) , and the cast of the areas of rectangles , where the household of the rectangle is any(prenominal) teentsy foster ( truth) , and the efflorescence is set by the convergence point of the stop number pocketbook of the rectangle that is the represent of essential dumbfound in the middle. Accordingly, we see formulas areas -
for the trapezoidal rule :
,
manner for mediocre rectangles :
figure . 1. curving trapezoid .
Fig . 2 . os trapezium system .
Fig . 3 . swayer of second-rate rectangles.
By the trapezoidal mode and second-rate rectangles singly intrinsic equals the mid advert of squares angulate trapezoids , where the beggarly of the trapezoid is whatever teensy judge (trueness) , and the cast of the areas of rectangles , where the household of the rectangle is any(prenominal) teentsy foster ( truth) , and the efflorescence is set by the convergence point of the stop number pocketbook of the rectangle that is the represent of essential dumbfound in the middle. Accordingly, we see formulas areas -
for the trapezoidal rule :
,
manner for mediocre rectangles :