Area of integration, help plz (1 Viewer)

[ghostman_on_3rd]

Calculate the area of the region bounded by:
y=1/x^2 + 2
y= -2x+5
x = 4


Answers were not given

Thanks in advance.

 

[ghostman_on_3rd]

EDIT: Thought maybe i'd explain a few things. The reason you don't integrate straight between the point of intersection of the two curves (x=1) and the boundary x = 4 is because the area produced is not uniform. If you were to sketch the situation, you would see that from 1 to 5/2 (where the straight line cuts the x-axis) is one uniform area between the two curves. From 5/2 to 4 and the x-axis is uniform for the 1/x^2 + 2 graph so you only have to integrate that. Hope this makes sense.

mmm
But if you find the area of y=1/x^2+2. Isnt that = area in between the graph and y =2 ?

as y = 2 is an asymptote of y= 1/x^2+2

 

[gurmies]

mmm
But if you find the area of y=1/x^2+2. Isnt that = area in between the graph and y =2 ?

as y = 2 is an asymptote of y= 1/x^2+2

Hmm, good point. I'm not too sure about this actually. On second thoughts, i'm quite sure you can't integrate over an asymptote.

 

[shaon0]

Hmm, good point. I'm not too sure about this actually. On second thoughts, i'm quite sure you can't integrate over an asymptote.

I don't think you can't integrate over an asymptote as the area will be undefined at a point. But I maybe wrong entirely.

 

[shaon0]

Can't say. At this point it remains trivial, although i'm leaning towards it not being able to be integrated. Then that means the question is void, does it not?

EDIT: Actually, maybe just integrate from the curve to y = 2 line and then add the rectangle below as it's a constituent of the whole area? Not sure..

You could take a limit as the function approaches the asymptote and integrate to infinity but that's too complicated and not necessary since gurmies has already got the solution. Should just wait for Trebla.

 

[lolokay]

 

[gurmies]

looks about right

 

[ghostman_on_3rd]

ye you're right!
I understand it, thanks !

 

[kevda1st]

ye you're right!
I understand it, thanks !

i showed u in class today lawrence...

 

[ghostman_on_3rd]

i showed u in class today lawrence...

You did, but i didnt accept it that day

but ye i do understand it and theres also another method for this but longer
.....im guessing your demanding a thanks from me lol?

thanks =p

 

[Gibbatron]

Drawing a diagram will always help because you can see what you have to integrate.