lanedance said:Hi Prince
I'm not sure I understand your question, can you elaborate?
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= ey/5.Princeofdark said: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?
The disk method is a mathematical technique used to find the volume of a solid of revolution by rotating a region bounded by a function around a vertical or horizontal axis. It is based on the idea that the volume of the solid can be approximated by an infinite number of thin disks stacked together.
To set up the integral for the disk method, you first need to determine the limits of integration by finding the points of intersection between the function and the axis of rotation. Then, you square the function and multiply it by π to get the cross-sectional area of each disk. Finally, integrate the cross-sectional area from the lower limit to the upper limit to find the total volume.
No, the disk method can only be used for finding the volume of solids of revolution with circular cross-sections. If the solid has a different cross-sectional shape, other methods such as the shell method or the washer method would need to be used.
Some tips for solving volume with the disk method include carefully choosing the axis of rotation to make the integral easier, breaking down the solid into smaller sections if necessary, and checking your work by using other methods such as the shell method. It is also important to pay attention to units and to use the correct formula for the cross-sectional area.
No, the disk method can only be used for finding the volume of solids of revolution with a known function and a known axis of rotation. If the solid is irregular or does not have a known function, other methods such as the method of cross-sections would need to be used.