Calculating Volume of Rotated Region in Quadrant 1

[Aerosion]

Homework Statement

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

Homework Equations

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.

 

[Hootenanny]

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

 

[Aerosion]

Yes yes, the x axis. Sorry.

 

[Hootenanny]

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.

 

[Aerosion]

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

 

[Hootenanny]

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

No worries