# Calculating Volume of Rotated Region in Quadrant 1

• Aerosion
In summary, the conversation discusses finding the volume of a solid formed by rotating a region in the first quadrant, enclosed by the equations y = x^2 and y = 2x, around the x-axis. The correct solution involves using the formula V = pi * integral from 0 to 2 of |(x^2)^2 - (2x)^2| dx. It is also suggested to sketch the two curves for a better understanding of the problem.

## Homework Statement

Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by
y = x^2
y = 2x

## The Attempt at a Solution

Okay, so I first solved both equations for y, which gave me x=radical(y) and x=y/2. Then I graphed both of them, found that the radical one was above the y/2, so I made the equation pi*(radical(y)^2 - (y/2)^2. I then made that equation a definite integral with lower limit 0 and upper limit 2.

Of course, it turned out wrong (I'd use Latex to make it look nice, but it's not coming out very well right now and I don't have the patience). Suffice it to say, I did something wrong somewhere.

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About which line are you rotating the region about, the x axis?

Yes yes, the x axis. Sorry.

Then there is no need to solve for x. The volume of revolution about the a axis of a region bounded by two functions, f(x) and g(x) and the lines x=a and x=b is given by;

$$V=\pi\int_a^b{\left|\left[f(x)\right]^2-\left[g(x)\right]^2\right|}dx$$

It my also be a good idea to sketch the two curves to get a visual idea of what your are actually doing.

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Ah okay, now I'm getting the right answer. Thanks.

Aerosion said:
Ah okay, now I'm getting the right answer. Thanks.
No worries