As the title says I need to calculate the area of the region enclosed by a certain curve which is the union of 4 curves in that form :
$\alpha$ : [-1,1] $\to$ $\mathcal R^2$ , $\alpha_1$($t$) = $t^2$ , $\alpha_2(t)$ = $2-t^2$
Now this is not exactly one of the curves of the exercise but an example. I need to understand if I can just sum up all of the areas by using this :
A = $\int ydx$ where in the example it should be $\int_{-1}^1 ((2-t^2)*2t)dt$
Moreover making a purely graphical reasoning I can confirm the result found analytically.
Thanks in advance for the help.