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Answer the following True or False. Let be a increasing positive function. Then the right endpoint approximation is greater than the area under the curve. True False
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Q. Answer the following True or False. Let be a increasing positive function. Then the right endpoint approximation is greater than the area under the curve. True False
- Definition of Right Endpoint Approximation: Let's consider what a right endpoint approximation is. When we approximate the area under the curve of a function using rectangles, the right endpoint approximation means that for each rectangle, the height is determined by the value of the function at the right endpoint of the interval. Since is an increasing function, the value at the right endpoint will always be greater than or equal to the value at any other point within the interval. This means that the area of each rectangle in the right endpoint approximation will be greater than or equal to the actual area under the curve for that interval. Therefore, when we sum up all the rectangles to approximate the total area under the curve, the right endpoint approximation will give us a value that is greater than or equal to the true area under the curve.
