Finding Volume of Solid Rotated X-Axis

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SUMMARY

The volume of the solid formed by rotating the line f(x) = 2x - 1 around the x-axis from x = 0 to x = 3 is calculated using the disk method. The correct setup for the integral is V = π ∫[0 to 3] (2x - 1)² dx. The previous incorrect answer of 46.0766 indicates a miscalculation in the integration process. The correct volume, after evaluating the integral, is 18π or approximately 56.5487.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with the disk method for volume calculation
  • Knowledge of polynomial functions and their graphs
  • Ability to perform definite integrals
NEXT STEPS
  • Review the disk method for calculating volumes of solids of revolution
  • Practice evaluating definite integrals with polynomial functions
  • Explore applications of integration in calculating areas and volumes
  • Learn about alternative methods such as the shell method for volume calculation
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Students studying calculus, educators teaching integral calculus, and anyone interested in solid geometry and volume calculations.

Cheapo2004
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Ok, I'm supposed to found the volume of the solid that is created after rotating the line f(x) = 2x-1 around the x axis. The limits are y=0 x=3 and x=0. I've been trying for about and hour, and keep getting the answer: 46.0766. I've done the integration tons of times, splitting the problem into two parts for each separate cone, and other stuff. I just can't seem to get the right answer, please help.
 
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