The results obtained are greater than which among the following?a)Pris...
Introduction
The question is asking which among the given methods (Prismoidal rule, Trapezoidal rule, Rectangular rule, and Square rule) yields results that are less than the others.
Explanation
To determine the answer, let's briefly discuss each method and compare their accuracy.
1. Prismoidal Rule
The prismoidal rule is a numerical integration method used to calculate the volume of irregular solids. It divides the solid into a series of prisms with trapezoidal cross-sections. The volume of each prism is then calculated using the trapezoidal rule and summed to obtain the total volume. The prismoidal rule provides a more accurate result than the trapezoidal rule.
2. Trapezoidal Rule
The trapezoidal rule is a simple numerical integration method that approximates the area under a curve by dividing it into trapezoids. It assumes a linear interpolation between the data points and sums the areas of the trapezoids to estimate the total area. The trapezoidal rule provides a less accurate result compared to more advanced methods like the prismoidal rule.
3. Rectangular Rule
The rectangular rule, also known as the midpoint rule, is another numerical integration method that approximates the area under a curve. It divides the area into a series of rectangles, with the height of each rectangle determined by the function value at the midpoint of the interval. The rectangular rule provides a less accurate result compared to the trapezoidal rule.
4. Square Rule
The square rule is not a well-known numerical integration method. It is not commonly used in engineering calculations and is not as accurate as the other methods mentioned above.
Conclusion
Comparing the accuracy of the methods, the trapezoidal rule provides less accurate results than the prismoidal rule. Therefore, the correct answer is option 'B' - the results obtained using the trapezoidal rule are greater than those obtained using the other methods mentioned.
The results obtained are greater than which among the following?a)Pris...
Due to the presence of curvature at the boundary whether it may be concave or convex towards the base line, the results are depended. It makes them greater than that obtained from the trapezoidal rule.