Lesson: Area Enclosed by Parametric Curves

Mathematics

In this lesson, we will learn how to use integration to find the area under a curve defined by parametric functions.

Sample Question Videos

  • 04:39

Worksheet

Q1:

Consider the curve defined by the parametric equations π‘₯=2𝑑cos and 𝑦=3𝑑sin.

Find ο„Έβˆ’6𝑑𝑑sind.

Find the area under the curve when 0β‰€π‘‘β‰€πœ‹.

Now, by taking 0≀𝑑≀2πœ‹, find the total area inside the curve.

Q2:

Consider the curve defined by the parametric equations π‘₯=π‘οŠ© and 𝑦=4βˆ’π‘οŠ¨.

Find the area under the curve where 0≀𝑝≀1.

Find the area under the curve where 0≀𝑝≀2.

Q3:

Determine the area trapped between the π‘₯-axis and the curve with parametric equations π‘₯=π‘‘οŠ© and 𝑦=𝑒 on the interval [0,1]. Approximate your answer to the nearest one decimal place.
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