Solving Volume with the Disk Method: Graph & Tips

[Princeofdark]

http://www.webassign.net/www14/symImages/5/5/e52c6d3f5c64e9f5bf52f9a215f4f2.gif

V = (pi)(r^2)


I tried to graph this but it seemed like the graph kept going. what do i do?

 

[lanedance]

Hi Prince

I'm not sure I understand your question, can you elaborate?

 

[Princeofdark]

Hi Prince

I'm not sure I understand your question, can you elaborate?

Consider the solid obtained by rotating the region bounded by the given curves about the y-axis.

http://www.webassign.net/www14/symImages/5/5/e52c6d3f5c64e9f5bf52f9a215f4f2.gif

Find the volume V of this solid.


^^

So basically that's the question and i can't solve it.

i started of by trying to draw in my graphing calculator, but the graph kept going.



So i need to find the volume, can you help me?

 

[lanedance]

I would try graphing y = ln5x, this function is negative for x<1 and diverges to negative infinity as x heads to 0, so only plot for x>0

Then try drawing on paper the region you want to rotate, and how it is rotated.

Solving for the volume will involve setting up an integral. Can you write down the volume for an infintesimally thick disk?
dV = r(y)^2.dy
wher r(y) is the radius of the disk

As the function is rotated around the y-axis it may help to re-write your function as x in terms of y

 

[HallsofIvy]

http://www.webassign.net/www14/symImages/5/5/e52c6d3f5c64e9f5bf52f9a215f4f2.gif

V = (pi)(r^2)


I tried to graph this but it seemed like the graph kept going. what do i do?

What do you mean by "the graph kept going"? The left boundary is x= 0, the y axis; the right boundary is the graph of y= ln(5x)= ln(5x); the lower boundary is y= 3; and the upper boundary is y= 5. Rotating around the x axis, the radius, r is x in y= ln(5x). That is, r= x= e^y/5.