# Homework Help: Volume integration using washermethod

1. Sep 27, 2008

### peercortsa

volume integration using "washer method"

1. The problem statement, all variables and given/known data
The region R bounded by y = x$$^{2}$$, y = 0, x = 1 and x = 4 is rotated about x = −1

2. Relevant equations
i know that these equations take on the form of $$\pi\int_a^b \\((outer radius)^{2} - (inner radius)^{2})\\,dx$$

3. The attempt at a solution
so i set the problem up like this and still cant get the correct answer which is $$339\pi/2$$

-for the bounds i know that the integral i want to evaluate is between 0 and 16 based on the line y=0 and the function $$y=x^{2}$$ evaluated at x=4.

-the outer radius is $$1+\sqrt{y}$$ and the inner radius is just 1

$$\pi\int_0^{16}\\ (1+\sqrt{y})^2-(1)^2\\,dy$$

Last edited: Sep 27, 2008
2. Sep 27, 2008

### tiny-tim

Welcome to PF!

Hi peercortsa! Welcome to PF!

That's right … but then your thickness is dx, so that's what you must integrate over …

∫(blah blah) dx, where blah blah is entirely a function of x.

3. Sep 27, 2008

### peercortsa

so..... did i even set up the equation correctly cuz i still cant seem to get the right answer no matter what i try

4. Sep 27, 2008

### tiny-tim

Your π∫…dx is correct for the area

but you still need to put the height inside the ∫ to make the volume.

Have a go!