Final answer:
To find the area enclosed by the curves y=x and y=2x, set the two equations equal to each other to find the intersection point. Then, integrate the difference between the two curves over the interval to find the area.
Step-by-step explanation:
To find the area enclosed by the curves y=x and y=2x, we need to find the points of intersection and integrate the difference between the two curves over that interval.
The intersection points can be found by setting the two equations equal to each other:
x = 2x
x = 0
So the curves intersect at x = 0. Now we can integrate the difference between y=2x and y=x over the interval [0, 2]:
Area = ∫(2x - x) dx from 0 to 2
Area = ∫x dx from 0 to 2
Area = [x^2/2] from 0 to 2
Area = (2^2/2) - (0^2/2) = 2 square units.