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Free Midpoint Rule calculator - approximate the area of a curve using Midpoint Rule (Riemann) step-by-step
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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.
Use the midpoint rule to estimate [latex]{\displaystyle\int }_{0}^{1}{x}^{2}dx[/latex] using four subintervals. Compare the result with the actual value of this integral.
The Composite Midpoint Rule. Using the Midpoint Rule on each interval and summing gives a formula that could be familiar: M n := f ( x 0 + x 1 2) h + f ( x 1 + x 2 2) h + ⋯ + f ( x n − 1 + x n 2) h = f ( a + ( a + h) 2) h + f ( ( a + h) + ( a + 2 h) 2) h + ⋯ + f ( ( b − h) + b 2) h = [ f ( a + h / 2) + f ( a + 3 h / 2) + ⋯ + f ( b − h / 2)] h.
Use this online midpoint rule calculator for computing the table of integrals of the given function over the interval (a, b) using the midpoint formula. This rule uses the midpoint of every interval as the point at which it evaluates the given function for the Riemann sum.
1 (a) Numerically approximate the integral by using the midpoint rule with m = 1, 2, 4, 8, and 16 subintervals. 1 (b) Find the analytic value of the integral (i.e. find the "true value").
