# Thread: Sketch the set Ta and find its area

1. ## Sketch the set Ta and find its area

I know the answer to this question (area Ta = (2/3)(a^(3/2))), but I'm somewhat confused as to how to approach it. Any help getting started would be appreciated.

Let "a" be an element of the set of all positive real numbers, and let Ta be the set of all points (x,y) such that 0 ≤ x ≤ a and 0 ≤ y ≤ x^(1/2). Sketch the set Ta and find its area.

Any help is much appreciated, thanks.

2. Originally Posted by ricketycricket
I know the answer to this question (area Ta = (2/3)(a^(3/2))), but I'm somewhat confused as to how to approach it. Any help getting started would be appreciated.

Let "a" be an element of the set of all positive real numbers, and let Ta be the set of all points (x,y) such that 0 ≤ x ≤ a and 0 ≤ y ≤ x^(1/2). Sketch the set Ta and find its area.

Any help is much appreciated, thanks.
fundamental theorem of calculus ...

$\displaystyle \displaystyle \int_0^a x^{\frac{1}{2}} \, dx = \left[\frac{2}{3}x^{\frac{3}{2}}\right]_0^a = \frac{2}{3}a^{\frac{3}{2}}$