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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.

Glossary

graph

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

integration

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-