This is the definition given on page 547 of the book 2. Consider the following s

Question

This is the definition given on page 547 of the book

2. Consider the following situation. Joey wants to derive a formula for the surface area of a right circular cylinder with radius r (r>0) and height h (h>0) by using the definition given on page 547 of the book. So, he decides to compute the exact surface area of the surface obtained by rotating the curve y =-r where 0 x h about the x-axis. When he does this he obtains dy dr=| 2x(-r)'/I+(0)'dr=-2 dr=-LTrh. In the end, Joey is quite dr cne becae end iathatyields anegaiveufe arca. (a) What is the issue with Joey's derivation? (b) How could you fix Joey's derivation?

Explanation / Answer

The condition of this theroem is that y=f(x) should be positive and have continous derivative.

(a) joy has take wrongly y=-r, this means y(=f(x)) is negative.

(b) he should have to take y=r

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