The Arc Length Of A Curve In Parametric Equations

HelpNeeder

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But doesn't the integral mean that we are calculating the area under the curve?

Thank you in advance.
 
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But doesn't the integral mean that we are calculating the area under the curve?

Thank you in advance.
Integration is actually a special type of addition.

You can add up small "areas" to get area under the curve.

You can add up small "lengths" to get "arc length".

It all depends on - what are you adding up by integrating.
 
"Area under the curve" is on specific application of the integral. It is typically the first application since it is the simplest but there are many other, more useful, applications of the integral.
 
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