Double Integral Bounds?

Question

Integrate (area integral) x*y dA where R is the region bounded by the graphs of y=(x)^1/2, y=(x/2), x=2 and x=4 would the bounds for x be 2 (lower) to 4 (upper) and the bounds for y be (1/2) (lower) (x)^(1/2) (upper) ?

Area Integral = Double Integral

Answer 1

I assume you just made a typo and meant to say (x/2) (lower).

You are right, assuming you are setting up the integral with the dy integral on the inside and dx on the outside.

Answer 2

If dA = dy dx the y limits are [ x /2, sqrt x] and x limits are [2 , 4] You dropped the x when you typed your lower limit for y.