# Area under curve given a set $\{ [x, y] \in \mathbb{R^2} \ | \ 0 \le x \le 1 \ \& \ 0 \le y \le x \arctan^2 x\}$

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 $$y$$?

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