How Do You Calculate Arc Length and Volume of Rotated Solids in Calculus?

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SUMMARY

The discussion focuses on calculating the volume of a solid of revolution and the arc length of a curve in calculus. The first problem involves finding the volume of the solid formed by rotating the region bounded by the curves y=x² and y=x³ from x=0 to x=1 around the x-axis, which can be solved using the disk method. The second problem requires calculating the arc length of the curve y=cosh(x) between the points (0,1) and (1,e²+1/2e), which utilizes the arc length formula. Participants emphasize the importance of understanding the concepts rather than rushing to meet deadlines.

PREREQUISITES
  • Understanding of the disk method for calculating volumes of solids of revolution
  • Familiarity with the arc length formula in calculus
  • Knowledge of hyperbolic functions, specifically cosh(x)
  • Basic integration techniques for evaluating definite integrals
NEXT STEPS
  • Study the disk method for volume calculations in calculus
  • Learn the arc length formula and its applications
  • Explore hyperbolic functions and their properties
  • Practice definite integrals involving polynomial and hyperbolic functions
USEFUL FOR

Students studying calculus, educators teaching mathematical concepts, and anyone seeking to improve their problem-solving skills in volume and arc length calculations.

Undercover.Terrorist
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i have 2 calculus questions that are due in the next half n hour and i have no idea how to even start them. I hope somoene can help me in time.

Question1
Find the volume of the solid obtained if the plane region E bounded by the curve y=x^2 and y=x^3 between x=0 and x=1 is rotated about the x-axis

Question2
Find the length of the curve y=coshx between points (0,1) and (1,e^2+1/2e)

If anyone can help me...i need the solutions quickly...thanks in advance
 
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I think you're misunderstanding the purpose of these forums.

If you truly want to learn the material, forget the homework deadline. You already dug your own grave anyway, by waiting until the last half hour (not that I'm condemning this - we've all been there).

Instead, work out what you can with the problems, show us what you've gotten so far, and somebody will surely jump in and guide you further.
 
don't worry about it..i figured it out for myself.
 

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