Debate about area bounded by equations.

Question

I'm doing a math assignment together with a friend and there is a question:

(a) The region $R$ is bounded by the curve $y=x^{2}$, the line $2x+y = 15$ and the $x$-axis. Find the area of $R$.

We're currently debating on which area is correctly shaded as region $R$.

My answer is: my answer

My friend's answer: my friend's answer

I'm pretty sure my answer is correct but my friend insists on his. Could anyone help us solve the debate?

Answer 1

Although you seem to be right, your friend does have a valid point by questioning the whole sense of a region, bounded by equations.

Therefore you might ask the following to your teacher: in this case, would the area $R$ be the dark green area, the light green one, both greens together, do you need to add the yellow and what about the orange?

Good luck