Question

Calculus volume question.
Let R be the region in the first quadrant bounded by the graphs of y=√x and
y = x/3. The Region R is the base of a solid. For this solid, the cross sections perpendicular to the y-axis are squares. Find the volume of this solid.

Answer 1

My question is, does it matter whether I integrate this in terms of x or y since the cross sections are squares?

Answer 2

What matters is that you can define your base area (x, or y, whichever it more convenient) and that you can properly define the cross section.

In this problem, the cross section does not vary with x. The cross section varies with the difference between two x's - in other words, with y.

Answer 3

Ah, so I must solve for x for the original functions and integrate over y correct?

Answer 4

yup

Answer 5

Ok, thanks!