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When a curve is described by parametric equations, say x=f(t) and y = g(t), then the area under this curve between given limits may be found by integration. The following applet approximates the area bounded by the parametric curve defined by x=x(t) and y=y(t) for a ≤ t ≤ b. Simply enter the functions x(t) and y=y(t) and the values a, b (in radians) and 0 ≤ n ≤ 1,000, the number of subintervals. The values a and b can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the x-axis in radians (i.e. multiples of \pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Software/Applets used on this page

David Little
This page uses an applet from David Little (Lecturer in the Mathematics Department, Penn State University, USA) and is used with his permission.



A diagram showing a relationship between two variables.
The diagram shows a vertical y axis and a horizontal x axis.


the process of finding an integral, the reverse process to differentiation.

parametric equations

a pair of equations x=u(t) and y=v(t) where t is a parameter, that describe a curve.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AP Calculus BC (USA)4IntegrationParametric integration-
AQA A-Level (UK - Pre-2017)C4IntegrationParametric integration-
CCEA A-Level (NI)C4IntegrationParametric integration-
Edexcel A-Level (UK - Pre-2017)C4IntegrationParametric integration-
Methods (UK)M9IntegrationParametric integration-
OCR A-Level (UK - Pre-2017)C4IntegrationParametric integration-
OCR-MEI A-Level (UK - Pre-2017)C4IntegrationParametric integration-
Pre-U A-Level (UK)5IntegrationParametric integration-
Universal (all site questions)IIntegrationParametric integration-
WJEC A-Level (Wales)C4IntegrationParametric integration-