Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose I have two function $f(x)$ and $g(x)$ such that for $x \in (\alpha, \beta )$ we have $f(x) \ge g(x) $.

I found an "exercise solution" that state that the volume given by the rotation of the area between $f$ and $g$ is:

$$\pi\int_\alpha^\beta (f(x) - g(x))^2 dx$$

but i think it's wrong and that it should be:

$$\pi\int_\alpha^\beta f(x)^2 - g(x)^2 dx$$

Who is right?

share|improve this question

1 Answer 1

up vote 1 down vote accepted

I'll assume that one of the candidates is the correct solution. Now, what is the volume of a cylindrical shell of radii $R>r$ and height $1$? It is the difference $$ \pi R^2 - \pi r^2 = \pi \left(R^2-r^2 \right). $$ This does not coincide with $\pi \left( R-r \right)^2$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.