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

Students will be able to

Q1:

Consider the curve defined by the parametric equations 𝑥=2𝑡cos and 𝑦=3𝑡sin.

Find −6𝑡𝑡sind.

Find the area under the curve when 0≤𝑡≤𝜋.

Now, by taking 0≤𝑡≤2𝜋, find the total area inside the curve.

Q2:

Consider the curve defined by the parametric equations 𝑥=𝑝 and 𝑦=4−𝑝.

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 𝑥-axis and the curve with parametric equations 𝑥=𝑡 and 𝑦=𝑒 on the interval [0,1]. Approximate your answer to the nearest one decimal place.

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