Parametric Integration

From 0:19 onwards: https://www.youtube.com/watch?v=ZBIH8LVbbzQ

Why are we considering the limits of t that correspond to both x & y values and not only x values? Isn't that like integrating a cartesian equation with both x and y limits instead of just x limits?

Reply 1

mqb2766

Original post by Pyruvic Acid

Your description of x and y limits is a bit misleading, as for that example you could consider the usual cartesian integral from x=0 to the x-axis crossing point, rather than doing a parametric integral.
But parametric equations / integrals can be used for regions which are not described by functions in cartesian coordinates - a circle for instance.