Computing Area Between Curves/Lines Part I

[Hckyplayer8]

I treated y=2x as f(x) and y=x as g(x). I plotted the functions over the interval and shaded the desired area. Next I found the antiderivatives in regards to x. Finally I plugged in the upper and lower limits and found their difference.

Does all look well?

 

[Steven G]

It looks fine. My only question is why did you not compute 2x-x = x before integrating?
Another thing is that you can figure out the area without calculus or to check your calculus. Just look at your graph.

 

[Hckyplayer8]

It looks fine. My only question is why did you not compute 2x-x = x before integrating?
Another thing is that you can figure out the area without calculus or to check your calculus. Just look at your graph.

Yeah. Should've saw that one.

Thanks Jomo.

 

[Steven G]

Just to be sure sure you know what is going on can you please tell me what is the exact area between those lines equal?

 

[Hckyplayer8]

Just to be sure sure you know what is going on can you please tell me what is the exact area between those lines equal?

The area equals the definite integral of a region bounded by the two, continuous functions and their limits.

Because both functions are found in the positive, positive plane, the area of y=2x includes the area of y=x. Thus one has to find the difference of the two areas to find the area of the desired bounded region.

After finding the appropriate antiderivatives, plugging in the limits to find the area and finding the differences of those areas, the desired area is 4.

 

[Steven G]

The area equals the definite integral of a region bounded by the two, continuous functions and their limits.

Because both functions are found in the positive, positive plane, the area of y=2x includes the area of y=x. Thus one has to find the difference of the two areas to find the area of the desired bounded region.

After finding the appropriate antiderivatives, plugging in the limits to find the area and finding the differences of those areas, the desired area is 4.

I was hoping that you would say 4 square units.