But i don't understand "with right hand rule".What do you mean?DemiMike said:
HallsofIvy said:
The Right Hand Rule is a method for approximating the value of a definite integral by dividing the interval into equal-width subintervals and using the right endpoint of each subinterval as the height of a rectangle. The sum of these rectangles represents an approximation of the integral, with a more accurate result achieved by using a greater number of subintervals.
The Right Hand Rule is typically used when the function being integrated is non-negative on the interval of integration, as the right endpoints of the subintervals will always give a conservative estimate of the integral's value. It is also useful for functions that are not continuous or are difficult to integrate analytically.
The Right Hand Rule is limited by the fact that it only provides an approximation of the integral, and the accuracy of the approximation depends on the number of subintervals used. It is also only applicable to functions that are non-negative on the interval of integration.
As the number of subintervals used in the "Right Hand Rule" increases, the width of each subinterval decreases, resulting in a closer approximation to the actual value of the integral. This is because smaller subintervals better capture the shape of the function being integrated and reduce the amount of area that is over or under-estimated.
Yes, there are other methods for evaluating definite integrals, such as the Left Hand Rule, Midpoint Rule, and Trapezoidal Rule. Each of these methods has its own advantages and limitations and may be more suitable for certain types of functions or intervals. It is important to understand and be able to apply multiple methods in order to obtain more accurate results.