Disk Washer Method Calc homework. Please help Im stuck?

Using the disk/washer method write the volume of the solid obtained by the region enclosed by y=x^(1/2), x=4 and y=0 about the y-axis as a definite integral. Do not evaluate the integral!!! Please helpDisk Washer Method Calc homework. Please help Im stuck?
Yeah, you could do it that way. But there's a much easier way.


It's known as the shell method, and by adding up an infinite number of shells made by this region... we can find the volume of the figure.


Imagine a shell, looks like a cylinder, but it's hollow. Think of what what would happen if you wanted to find the volume of that shell. You could cut it right down the middle and add up the volume of a rectangular prism: (Length)(Width)(Height/Thickness). The length is the circumference of the rotation, or 2蟺(r)... or what's on top - what's on bottom.


In this case, the function on top is x^(1/2), and that on bottom is 0. So, top - bottom is x^(1/2) - 0.


Let's setup our integral


2蟺鈭?x^(1/2)-0)(width)(height/thickness鈥?br>

Remember, the length is the circumference.


The width is the distance from the of rotation to the farthest point right. Well, in this case it would be 4, but it's necessary to call the out most part x. The width is always achieved by right - left. Or x - 0, remember the y axis is really x=0.


Substitute our width into the integral:


2蟺鈭?x^(1/2)-0)(x-0)(height/thickness)


That leaves our height/thickness, and the only thing left is our dx... because we're adding up an infinite number of these shells. The one point represents each shell we add up. In addition, our bounds would be from x=0 to x=4... just like if you were to slice a cross section perpendicular to the x-axis.


So...


2蟺鈭?x^(1/2)-0)(x-0)dx from x=0 until x=4.


I know it's a little confusing, but if you need any more help please feel free to give me an IM or email at sparta308@yahoo.com.

worms