Final answer:
To compute the double integral ∬D(62xy−x ²)dA over the given region, we need to find the limits of integration in terms of x and y. The limits of integration for x are 0 to 1, and for y, the lower limit is x² and the upper limit is √x. The integrand is (62xy−x ²).
Step-by-step explanation:
To compute the double integral ∬D(62xy−x ²)dA over the region bounded below by y=x² and above by y=√x, we need to define the limits of integration in terms of x and y. The region D is defined by the intersection of the curves y=x² and y=√x. To find the limits of integration, we need to find the x-values at the points of intersection of these two curves. Setting the equations y=x² and y=√x equal to each other, we get x²=√x. Solving for x, we find that x=0 and x=1 are the x-values that define the region of integration.
Now, let's set up the double integral in terms of x and y. The limits of integration for x are from 0 to 1, and for y, the lower limit is x² and the upper limit is √x. The integrand is (62xy−x ²). Therefore, the double integral can be written as:
∬D(62xy−x ²)dA = ∫0ˡ∫x²ᵘ (62xy−x ²) dy dx.