Area between 2 curves helpppp (1 Viewer)

[littlesmallworld]

Calculate the area bounded by the curve f(x)= x^2, g(x)=1/x^2, x>0 and thr line x=3

 

[kev-kun]

Hopefully not wrong.

 

[littlesmallworld]

The answer is 8 square units

 

[Carrotsticks]

Hopefully not wrong.
View attachment 30031

You can't do difference of two functions for this one. You must break it up as one area from 0 to 1, then from 1 to 3.

 

[kev-kun]

You can't do difference of two functions for this one. You must break it up as one area from 0 to 1, then from 1 to 3.

Ahh.... I knew I did something wrong :/

@ littlesmallworld Should be 1 unit not 8

 

[littlesmallworld]

So then do i integrate 1/x^2 -x^2 from 0 to 1 then do the same for 1-3?

 

[Carrotsticks]

So then do i integrate 1/x^2 -x^2 from 0 to 1 then do the same for 1-3?

My equation didn't show for some reason.

Integrate x^2 from 0 to 1, and add that with the integral of 1/x^2 from 1 to 3.

 

[QZP]

With these types of questions, draw out (or picture) the graphs and determine how you can find out the area (usually it's just partialising the area depending on point of intersection). Then, it's all on your algebra for the following integrals.

 

[pHyRe]

You can't do difference of two functions for this one. You must break it up as one area from 0 to 1, then from 1 to 3.

phew, i was looking at that previous solution thinking i musta forgotten all my maths. lol

 

[kev-kun]

phew, i was looking at that previous solution thinking i musta forgotten all my maths. lol

Lol whoops my bad =='

 

[iloveschool1996]

hey carrotsticks how do u know its from 0 to 1 and 1 to 3? can u plz explain plz thanksss

 

[Carrotsticks]

hey carrotsticks how do u know its from 0 to 1 and 1 to 3? can u plz explain plz thanksss

Because according to the diagram, they intersect at some point. Solving the two curves simultaneously, x^2 = 1/x^2 and the solution is x=1.

So from 0 to 1 for the y=x^2 curve (as per the diagram) then 1 to 3 for the y=1/x^2 curve because the question gave 3 as the upper limit.

 

[pHyRe]

hey carrotsticks how do u know its from 0 to 1 and 1 to 3? can u plz explain plz thanksss

adding on to what carrot said, normally you would take the top curve minus the bottom curve to get the bit inbetween. But you can't really determine which curve is on top of the other in the area specified, right? So you have to break it into sections.

 

[littlesmallworld]

Umm.. I got 1 as the answer. But the textbook says 8. Am i doing something wrong?

 

[anomalousdecay]

My equation didn't show for some reason.

Its LaTex problems with the renderer (we just got a new one after the old one stuffed up).

If it persists, maybe report it to Brent again.