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

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.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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