# I Should we consider negative axis when finding the volume?

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1. Dec 21, 2016

### Phys12

Question:
Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified line. Sketch the
region, the solid, and a typical disk or washer.
y2 = x; x = 2y; about the y-axis

Now, when I solved the question, I multiplies the entire integral by 2 since the limits I took were from -2 to 2. However, in the answer, they have considered only the values above the x-axis and not below. Why is it so? It doesn't specify in the question that we need to find the area of only that region which lies above the x-axis.

2. Dec 21, 2016

### Staff: Mentor

This doesn't make any sense. The two curves intersect at (0, 0) and (4, 2). What does your integral look like?
The region that is being revolved around the y-axis is completely above the x-axis, except the point (0, 0). Did you sketch the region that is being revolved?

3. Dec 21, 2016

### Phys12

Okay, I got it. Just one question, when we plot x=y^2, why don't we plot it below the x-axis as well? I know that it will cease to be a function, but we can values for x when we take y and -y, right? (That's what got me confused, I plotted y^2=x as y=x^2 but turned 90 degrees. Which made me draw another line below the x axis as well for some reason-- stupid me!)

4. Dec 21, 2016

### Staff: Mentor

You do plot a part of it below the x-axis. But, the region that is being revolved is between this curve and the line x = 2y. That region is completely in the first quadrant.