Last question on integration (and i am stuck)

[JakePearson]

in plan view, the shoreline of a bay may be approximated by a curve f(x) = -x² + 2x between one headland at x = 0 and another at x = 1km, where (f) is also measured in km. at low tide, the edge of the sea just reaches each headland, following a straight line between them. calculate in km² the area of the bay uncovered by water at low tide?

does anyone get this ??

because i do not, whatsoever, i would try, but don't know where to start either let alone answer it :(

 

[Mark44]

Have you drawn a graph of the shore? Do you know what a headland is?

 

[JakePearson]

bare with me, i am a diagnosed dyslexic sorry, i know what a head land is, but i can not seem to go anywhere, I am not comprehending this info lol

 

[Mark44]

OK, then have you drawn a graph of the function f(x) = -x² + 2x?

Also, are you sure about the information you've given in this problem? The graph doesn't show any headland at x = 1 km.

 

[JakePearson]

that is what the question says on my sheet mate, I am sure i aint dyslexic and it is the bloody lectures that can't write down questions properly haha

 

[HallsofIvy]

I would assume that the bay curves from (0,0) to (1,1) so the area sought is between the graphs y= x and y= -x^2+ 2x.

$$\int_0^2 x-(-x^2+ 2x) dx$$

JakePearson, what is your purpose in telling us in one post that "i am a diagnosed dyslexic" and in the very next "im sure i aint dyslexic". If you are not dyslexic (and if you can spell "dyslexic" you probably aren't!) why tell us that you were diagnosed that way?

I see nothing wrong with the way the problem is given: there is one "headland" that extends to (0,0) and another that only extends to (1,1).

 

[Mark44]

OK, draw a graph, and assume that the lecturer meant to say that there was a headland at x = 2 km, (and write this down on your work that you hand in), and then work the problem. Other than the misinformation given, it's pretty straightforward.

 

[HallsofIvy]

OK, draw a graph, and assume that the lecturer meant to say that there was a headland at x = 2 km, (and write this down on your work that you hand in), and then work the problem. Other than the misinformation given, it's pretty straightforward.

Why assume that? Is there any reason to think that the line between headlands is the x-axis?

 

[Mark44]

Why assume that? Is there any reason to think that the line between headlands is the x-axis?

Yes. The graph of y = -x² + 2x naturally defines a bay with headlands at x = 0 and x = 2. the point at (1, 1) doesn't look much like a headland to me. In fact, it looks like the the point in the bay that is most inland, if that makes any sense.

I believe that there is a good chance that OP's lecturer erred in saying that there is a headland at x = 1.

 

[Bachelier]

Here's the graph...

WHy can't we just integrate the formula -x^2 + 2x between 0 and 1?