0
What are some methods to approximate the value of an integral when it cannot be calculated directly?
Wiki User
∙ 10y ago
There are two main methods.
One is the trapezium method. Here the integral ("area under the curve") is split into a large number of trapeziums with their parallel sides being vertical. The areas of these trapeziums are calculated and added together to approximate the integral. The greater the number of trapeziums the more accurate the answer but also the more effort is required.
Another approach, which can sometimes work, is to find two integrable functions such that one of them is greater than the function to be integrated and the other is less. If the required function can be tightly sandwiched between two such functions then the integral of the function will be between the integrals of the two integrable functions. Even if you cannot find two such functions that fulfil this requirement over the whole domain, provided you can find pairs of functions that do so over all but a finite number of points is good enough. Actually, I believe it works even if the number of gaps are countably infinite (cardinality Aleph null), but I am not sure of that.
Wiki User
∙ 10y ago
Add your answer:
Earn +20 pts
How do you find the approximate area?
There are many approximation methods for area.
Why you use simpson's method for integrating it can be done by simple integration method also?
Sometimes a function can't be integrated by regular methods, or just an estimate for the integral is needed. It's silly to use Simpson's Rule for a function such as cos(x) that has an elementary antiderivative, but something like e^(-x^2) doesn't. So, you can approximate the definite integral using Simpson's Rule.
How do you prove the general form of the quintic is not solvable?
A general quintic can be solved using numeric methods. It may be an approximate solution but then even the solution to x2 = 2, in decimal terms, is approximate.
What is the theory of finite differential method?
Finite Differential Methods (FDM) are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.
How do you spell caculate?
The correct spelling is calculated - to have determined by reasoning, logic, or mathematical methods.
How do you find the approximate area?
There are many approximation methods for area.
Why you use simpson's method for integrating it can be done by simple integration method also?
Sometimes a function can't be integrated by regular methods, or just an estimate for the integral is needed. It's silly to use Simpson's Rule for a function such as cos(x) that has an elementary antiderivative, but something like e^(-x^2) doesn't. So, you can approximate the definite integral using Simpson's Rule.
What is procurement performance?
Procurement performance is an activity or an integral component of integral procurement management. It involves in describing key indicators, methods, and processes that are necessary for measuring the procurement success.
What has the author F S Shaw written?
F. S. Shaw has written: 'An introduction to relaxation methods (Approximate methods of numerical computation)' 'An introduction to relaxation methods' 'Stress analysis of an engine mount'
What has the author George D Mouat written?
George D. Mouat has written: 'Methods of approximate integration'
Math class is an example of which class?
It is a static class; meaning that all the methods can be accessed directly from the class name, without instantiating an object.It is a static class; meaning that all the methods can be accessed directly from the class name, without instantiating an object.It is a static class; meaning that all the methods can be accessed directly from the class name, without instantiating an object.It is a static class; meaning that all the methods can be accessed directly from the class name, without instantiating an object.
How do you prove the general form of the quintic is not solvable?
A general quintic can be solved using numeric methods. It may be an approximate solution but then even the solution to x2 = 2, in decimal terms, is approximate.
What is the theory of finite differential method?
Finite Differential Methods (FDM) are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.
What has the author H Kreiss written?
H Kreiss has written: 'Methods for the approximate solution of time dependent problems'
How do you atomic radius of an element?
The atomic radius is calculated by spctroscopic or X-ray methods.
What activity is computed differently using the two methods of formatting a statement of cash flows?
Cash flow from operating activity is the only activity which is calculated using two different methods that is direct method and indirect method while other two cash flows are calculated in same manner in both of methods.
Methods of selling Pizza Hut in directly to the market?
it doesn't make sense
