Final answer:
To write the iterated integral for the given region bounded by y=√x, y=0, and x=4, we determine the limits of integration for x and y. The limits for x are 0 to 4, and the limits for y are 0 to √x. The iterated integral is then ∫04 ∫0√x dy dx.
Step-by-step explanation:
To write an iterated integral for ∫r dA over the region R bounded by y=√x, y=0, and x=4, we need to determine the limits of integration for both x and y.
First, let's determine the limits of integration for x. We know that the region is bounded by y=0 and x=4, so the limits for x are from 0 to 4.
Next, let's determine the limits of integration for y. The region is bounded by y=0 and y=√x. At any given x, the y-values range from 0 to the square root of x. Therefore, the limits for y are from 0 to √x.
Putting it all together, the iterated integral for ∫r dA over the region R is:
∫04 ∫0√x dy dx