If a curve is given in parametric form, is there any way that I can find the area bounded by the curve and the x-axis without finding $y$ as an explicit function of $x$?
Consider this curve for which $$y=a(1-\cos t)$$ and $$x=a(t-\sin t)$$
I need to find the area bounded by an arc of this curve and the x-axis.
Expressing $y$ in terms of $x$ would become a tedious job here.
The only thing I can make out is that $y=dx/dt$. Will it be of any help in this case?
Due to the parametric form, I am not able to draw an approximate graph of the function.
Can anybody help on the approach?