How Do I Solve for the Intersection Points of Bounded Equations?

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In summary, the task given is to find the volume of a solid formed by revolving the region bounded by the graphs of the equations y=2x^2, y=0, and x=2 about the indicated lines. This volume can be found by first finding the points of intersection between the given equations and then using calculus to calculate the volume. The question then asks for the volume when revolving around the y-axis, x-axis, and the lines y=8 and x=2. In order to find these volumes, the equations must be equated and the points of intersection must be determined.
  • #1
ISU20CpreE
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I have to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated lines.

[tex] y=2x^2 , y=0 , x=2 [/tex] It then wants me to figure out:

(a) the y-axis (b) the x-axis
(c) the line y=8 (d) the line x=2

In order to get the intersection points I need to equate the equations given to me. The problem is I really don't know how to equate the [tex] x=2 [/tex]
thats holding me to finish this problem. Please I need some advice.
 
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  • #2
You mean you're only having trouble with question d? It's not really clear to me where you're stuck. What have you done so far?
 
  • #3
Not clear what the question is asking. You have a surface area on the XY plane bounded by two straight lines and a hyperbola. What does it revolving around to generate a solid?
 
  • #4
You appear to be asking about the points of intersection of those three boundaries, but surely that's easy (If you are taking calculus).

The curves y= 2x2, y= 0 intersect at y= 0= 2x2 or x= 0, y= 0.
The curves y= 0, x= 2 intersect at (2,0), of course.
The curves y= 2x2, x= 2 intersect at (2, 2(2)2)= (2,8).
 

FAQ: How Do I Solve for the Intersection Points of Bounded Equations?

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