Evaluating the Accuracy of Strategies to Find the Area between a curve and two lines

[Larry Moats]

Would anyone be able to exhaustively justify why using the definite integral to find the area between the curve y = x³ - 9x² + 24x - 10, the y axis and the lines y = 6 and y = 26 is far more accurate than employing the trapezoidal and Monte Carlo method to this end.

thanks in advance

 

[Ishuda]

Both the trapezoidal and Monte Carlo method are approximations to the integral which is the exact answer. The trapezoidal and Monte Carlo methods are exact only under certain circumstances and for particular functions. The function given is not one of them.