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

Q1:

Consider the curve defined by the parametric equations π₯=2π‘cos and π¦=3π‘sin.

Find οΈβ6π‘π‘sindο¨.

Find the area under the curve when 0β€π‘β€π.

Now, by taking 0β€π‘β€2π, find the total area inside the curve.

Q2:

Consider the curve defined by the parametric equations π₯=πο© and π¦=4βπο¨.

Find the area under the curve where 0β€πβ€1.

Find the area under the curve where 0β€πβ€2.

Q3:

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

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