Calculus 2 volume integration, y=axis

[funkyguy4000]

Hello, so I've been having lots of trouble with a math problem.
I can differentiate functions but I'm kinda confused on what to do when it is like y=4

So say you have the given: y= x^2 and then y=4, x=0, x=2. Rotate about the y-axis.
I'm know you have to get it into respect to y so x=sqrt(y) but what would I do from there?! you can't put x in terms of y for y=4! I'm confused. Can somebody help me out or point me in the right direction.

 

[mathwonk]

they are giving you 4 different curves or lines and you are supposed to envision the region bounded by those curves or lines. so you have the line y=4 at the top, y=x^2 on the right, ...

ooops, your equations do not fit together to give one region. you need to re - read the question.

 

[funkyguy4000]

Okay well the y=x^2 is a parabola so it goes on both sides of the y-axis. And then the y=4 is another bounding line.

we are supposed to rotate the bounded region from x=0 to 2 around the y-axis.

I'm just confused on how to rotate it around like that.

 

[mathwonk]

well you don't want to say x=2 if you know y=4 and y = x^2. rather you should say y = x^2 for x≥0, y=4, and x=0. but if that's what it said, its their fault not yours.

so apparently the region is bounded by y = x^2 for x≥0, x = 0 and y=4. that makes it a portion of the right half of the parabola. then you rotate it around the y axis.


is that hard to see? your book may not be too well written.

 

[funkyguy4000]

well they give me the limits x=0 and x=2. y=x^2 and y=4 intersect at x=2.

I can imagine it. I'm just confused how to rotate it around the y=axis. what method to use and how to get the variables needed in the method. I tried the shells method and that didn't work. I didn't understand how to get the needed material.