# Lesson Worksheet: Area Enclosed by Parametric Curves Mathematics

In this worksheet, we will practice using integration to find the area under a curve defined by parametric functions.

Question 1

Consider the curve defined by the parametric equations and .

Find .

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Find the area under the curve when .

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Now, by taking , find the total area inside the curve.

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Question 2

Consider the curve defined by the parametric equations and .

Find the area under the curve where .

Find the area under the curve where .

Question 3

Determine the area trapped between the and the curve with parametric equations and on the interval . Approximate your answer to the nearest one decimal place.

Question 4

Determine the area trapped between the -axis and the parametric curve defined by the equations and on the interval .

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Question 5

Determine the area inside the curve defined by the parametric equations and .

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Question 6

Find the area between the following two curves: curve 1 that is defined by the parametric equations , and curve 2 that is defined by the parametric equations , on the interval .

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Question 7

Find the area between curve 1 defined by the parametric equations , and curve 2 defined by the parametric equations , on the interval .

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Question 8

Find the area between the following curves: curve 1 that is defined by the parametric equations , ; curve 2 that is defined by the parametric equations , ; and curve 3 that is defined by the parametric equation , .

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Question 9

Consider the curve defined by the parametric equations , , . Find the area between the curve and the on the interval . Approximate your answer to three decimal places.

Question 10

Consider the curve defined by the parametric equations , . Find the area between the curve and the on the interval .

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This lesson includes 72 additional question variations for subscribers.

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