Area under the curve of parametric equations

This article continues from the previous article. It may be a good idea to read through it before attempting this. This articles explores how to find the area.
We know that to find the area under the curve we integrate. That is we find;
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…or we could also use the chain rule;
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We shall look at some examples below.

Example

In this example we shall find the area under the curve of the parametric equations given below in the range of t=1 and t=2.
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We need to work out;
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We can see that;
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We can work out dx/dt because;
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That must mean that;
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Now we can find the integral in question;
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