Evaluate area under the curve for:

$\{ [x, y] \in \mathbb{R^2} \ | \ 0 \le x \le 1 \ \& \ 0 \le y \le x \arctan^2 x\}$

I know that to find the area under a curve of a function from a to b, I would just do $\int^b_a f(x)\ dx $

But how would I go about solving this, given a set?

If it is just $\int^1_0 f(x) \ dx$, what would be the $f(x)$ here to satisfy the inequalities for $y$?

  • 4
    $\begingroup$ The set you wrote is not a curve. It is a region whose area is $\int_{0}^{1}x\arctan^{2}x{\rm d}x$. $\endgroup$ – eranreches Jun 7 at 0:59

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