Math Is Fun Forum

I was doing my weekly physics homework but got stuck with 2 problems and then I will be done.

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Could anyone provide any insight as to how to solve this problems?

Today in my Calculus II class we went over how to find the surface area of a solid of rotation. The professor explained it in terms of:

Which Im not sure I really understand whats going on so Im going to have to do some extra reading etc which is fine. However, before doing surface area we were doing volume which I understood perfectly. You get the solid and you take a slice which is a circle itself so to get the volume you integrate the area function of the cross-section:

So for that formula we are using the area of a circle to find the volume of the solid by integrating. So right now if we are trying to find the surface area, why cant you use the circumference of a circle and integrate that? Such as:

While in the lecture I made the comment during the class and he told me that I cant do it like that and he gave no explanation...

Could anyone help me clarify this issue?

I was solving a problem which was to find the length of a parametric equation. I got it down to the first step in the picture and then got stuck. I checked on the online manual and thats how they put the last part. However, I do not understand how they removed the absolute value inside the integral and the 3a/2 becomes 6a?

I have to approximate ln(5) with n=10. Where n is the subintervals.

However, im not sure how to continue?

Let A be any set in which is a subset of some universal set U.

Prove that:

A intersection U = A

Now, I get the logic behind this and understand the statement. My problem is developing a proof for this. Could anyone help?

Rather than giving me the answer I would really appreciate some guidelines to follow please?

These are others that I also understand them but dont know how to generate a proof:

A union U = U

A intersection {} = {}