The trapezoidal rule is an approximation method used to estimate the definite integral of a function over an interval. It divides the area under the curve into trapezoids and sums up their areas to get an approximate total.
Imagine you have a bunch of differently shaped tiles, but you want to find out how much space they cover when arranged in a specific pattern. You can use trapezoids as placeholders for these tiles and add up their areas to get an estimate of the total area covered.
Approximation Method: An approximation method provides an estimate or close approximation rather than an exact solution. It's like using a ruler with markings instead of measuring with infinite precision.
Definite Integral: The definite integral calculates the net accumulation or total change of a quantity over an interval. It's like finding the exact sum of all those tile areas without any estimation.
Riemann Sum: A Riemann sum is another method for approximating integrals by dividing the area under the curve into rectangles instead of trapezoids.
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