Here are the essential concepts you must grasp in order to answer the question correctly.
Midpoint Rule
The Midpoint Rule is a numerical method used to approximate the value of a definite integral. It involves dividing the interval of integration into subintervals, calculating the midpoint of each subinterval, and then evaluating the function at these midpoints. The area under the curve is then approximated by summing the areas of rectangles formed by these midpoints, multiplied by the width of the subintervals.
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Definite Integral
A definite integral represents the signed area under a curve defined by a function over a specific interval [a, b]. It is denoted as ∫(a to b) f(x) dx and provides a way to calculate total accumulation, such as area, volume, or other quantities. The Fundamental Theorem of Calculus connects the concept of differentiation with integration, allowing for the evaluation of definite integrals using antiderivatives.
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Subintervals
Subintervals are smaller segments into which the main interval of integration is divided when applying numerical methods like the Midpoint Rule. The number of subintervals, denoted as 'n', affects the accuracy of the approximation; more subintervals generally lead to a better approximation of the integral. Each subinterval has a width calculated as (b - a) / n, where [a, b] is the interval of integration.
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