Determine k given that the enclosed region has area 16/3 units^2

Question

Lines:

y=k

y=x²

Answer: k= cube root of 16

Answer 1

Answer 2

You can start by drawing a graph for yourself. y = x^2 will give us a parabola and y = k will be a vertical line. Those lines along with the x-axis form an enclosed triangle that we are told has an area of 16/3 units^2. We can find the area of an enclosed region by integrating.

If we assume the integral has a lower bound of x = 0 (vertex of the parabola) and an upper bound of x = k, we can set up ∫x²dx.

When we integrate x² with respect to x, we get x³/3 and we will evaluate that from 0 to k. This will give us that (k³/3) - (0³/3) = 16/3 and solving this leads us to k = 16^1/3 (cubed root of 16, sorry I couldn't find the cubed root icon).