Right Endpoint
Right Endpoint - Related Videos
01:19
Precipitation Titration: Endpoint Detection Methods
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2025
In argentometric precipitation titrations, endpoints can be detected visually by the Mohr, Volhard, and Fajans methods. In the Mohr method, adding a soluble chromate indicator gives an initial yellow color to the analyte solution. As the titrant is added, the first excess of silver ions forms a red silver chromate precipitate, marking the endpoint. The solution pH should be maintained at about 8 by adding solid CaCO3. In the Volhard method, a standard excess of AgNO3 is first added to the...
07:05
Important Endpoints and Proliferative Markers to Assess Small Intestinal Injury and Adaptation using a Mouse Model of Chemotherapy-Induced Mucositis
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Cited by 9 •
2019
Here, we present a protocol to establish important endpoints and proliferative markers of small intestinal injury and compensatory hyperproliferation using a model of chemotherapy-induced mucositis. We demonstrate the detection of proliferating cells using a cell cycle specific marker and using small intestinal weight, crypt depth, and villus height as endpoints.
02:39
Indicators
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2020
Certain organic substances change color in dilute solution when the hydronium ion concentration reaches a particular value. For example, phenolphthalein is a colorless substance in any aqueous solution with a hydronium ion concentration greater than 5.0 × 10−9 M (pH < 8.3). In more basic solutions where the hydronium ion concentration is less than 5.0 × 10−9 M (pH > 8.3), it is red or pink. Substances such as phenolphthalein, which can be used to determine the pH of a solution, are called...
07:56
Determination of Carbonyl Functional Groups in Bio-oils by Potentiometric Titration: The Faix Method
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Cited by 5 •
2017
Here we present a potentiometric titration technique for accurately quantifying carbonyl compounds in pyrolysis bio-oils.
10:17
Introduction to Titration
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2023
Source: Laboratory of Dr. Yee Nee Tan — Agency for Science, Technology, and Research Titration is a common technique used to quantitatively determine the unknown concentration of an identified analyte.1-4 It is also called volumetric analysis, as the measurement of volumes is critical in titration. There are many types of titrations based on the types of reactions they exploit. The most common types are acid-base titrations and redox titrations.5-11 In a typical titration process, a standard...
FAQs
Choosing the greater-coordinate boundary of each subinterval determines where the function is sampled. That sampled value becomes the height of the corresponding rectangle, while the subinterval width determines its horizontal extent. Summing these rectangle contributions produces an approximation to the accumulated area, linking endpoint selection to the geometry behind Riemann sums.
Refining the partition reduces the width of the pieces used to construct the rectangles. Because the right-endpoint values are then taken over smaller subintervals, the resulting sum can move toward the exact definite integral. This limiting behavior is central to connecting a finite numerical estimate with the integral it is intended to approximate.
A partition breaks the original interval into multiple subintervals, and each subinterval has its own right boundary. The method evaluates the function at every one of those boundaries rather than using a single endpoint for the whole interval. This repeated sampling creates a sequence of rectangle heights that collectively represents the interval's accumulated area.
Start with the interval and divide it into subintervals. For each piece, identify its greater-coordinate boundary, evaluate the function there, and use that value as the rectangle height. Pair each height with the corresponding subinterval width, then add the rectangle contributions. Repeating the calculation with a finer partition gives a more refined estimate.
Right-endpoint sums are useful when a definite integral must be estimated numerically rather than treated only as a limiting object. They convert function values into rectangle areas and provide a finite approximation that can be compared with the exact integral. The same comparison supports error analysis by showing how approximation changes as the partition is refined.
In mathematics, the construction illustrates how Riemann integration builds an integral from sums over subintervals. Each sampled function value contributes a rectangle, and the limiting process explains why those finite sums can represent accumulated area. Thus, the technique gives a concrete geometric route from partitioning an interval to the analytic idea of a definite integral.