Another example of a Monte Carlo method, whereby a random process is used to find an approximation to a mathematical value, in this case the area under a curve y=x².
Choose a number of random points and click on Simulate. These points will be randomly placed on the graph space which is a unit square. The proportion of point under the curve gives an estimate of the area under the curve. (In theory, using integration methods, this area is 1/3.)
Software/Applets used on this page
Glossary
graph
A diagram showing a relationship between two variables.
The diagram shows a vertical y axis and a horizontal x axis.
The diagram shows a vertical y axis and a horizontal x axis.
integration
the process of finding an integral, the reverse process to differentiation.
This question appears in the following syllabi:
Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|
AQA A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
AQA AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
AQA AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
CBSE XII (India) | Probability | Probability | Repeated independent (Bernoulli) trials and binomial distribution | - |
CBSE XI (India) | Statistics and Probability | Probability | Random experiments, outcomes, sample spaces (set representation) | - |
CCEA A-Level (NI) | S1 | Probability | Experimental | - |
CIE A-Level (UK) | S1 | Probability | Experimental | - |
Edexcel A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
Edexcel AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
Edexcel AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
I.B. Higher Level | 5 | Probability | Experimental | - |
I.B. Standard Level | 5 | Probability | Experimental | - |
Methods (UK) | M15 | Probability | Experimental | - |
I.B. (MSSL) | 3 | Probability | Experimental | - |
OCR A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
OCR AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
OCR MEI AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
OCR-MEI A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
Pre-Calculus (US) | E4 | Probability | Experimental | - |
Pre-U A-Level (UK) | Prob | Probability | Experimental | - |
Scottish (Highers + Advanced) | HS | Probability | Experimental | - |
Scottish Highers | S | Probability | Experimental | - |
Universal (all site questions) | P | Probability | Experimental | - |
WJEC A-Level (Wales) | S1 | Probability | Experimental | - |