Volume of Generated Solid: y1=ex,y2=ex/2,x=ln(2),x=ln(3)

[Method]

The question is:

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Find the volume of the solid generated by revolving the plane region bounded by the given curves about x-axis. [FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Math-italic]e[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]/[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]ln[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]ln[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main];[/FONT]​

The two functions intersect only at x = 0, but I'm not completely sure where ln(2) and ln(3) come in.

Any help is appreciated.

 

[tkhunny]

Please show your setup.

As far as "x = a constant", consider your limits of integration.