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This tool will calculate the midpoint rule approximation of an integral for a given function, interval, and number of subintervals.
The Midpoint Rule is a numerical method used to approximate the value of a definite integral. It provides a way to estimate the area under a curve, which is particularly useful when the integral cannot be calculated directly.
Midpoint rule for definite integrals: Enter a function f(x), use the a and b sliders to choose the limits of integration, and use the n slider to increase the number of subintervals.
The formula of the midpoint rule of the given function is: a ∫ b f (x) dx= Δx/2 [f (x 0 +x 1 )/2+ f (x 1 +x 2 )/2+…+ f (x n-2 +x n-1 )/2+f (x n-1 +x n )/2] where Δx= (b-a)/n. f (x) is the function whose midpoint is required. a and b are the lower limit and upper limit respectively. Δx is the length of the subinterval.
midpoint rule. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music….
Free "Midpoint Rule Calculator". Calculate a table of the integrals of the given function f(x) over the interval (a,b) using Midpoint method.
