# Science:Math Exam Resources/Courses/MATH103/April 2013/Question 04 (b)

MATH103 April 2013
Other MATH103 Exams

### Question 04 (b)

Torricelli's Trumpet

The surface area of a solid of revolution obtained from revolving ${\displaystyle \displaystyle y=f(x)}$ about the x-axis for ${\displaystyle \displaystyle a\leq x\leq b}$ is given by ${\displaystyle \displaystyle A=2\pi \int _{a}^{b}y{\sqrt {1+{\big (}{\frac {dy}{dx}}{\big )}^{2}}}\,dx}$

Consider the surface area of the surface obtained by revolving ${\displaystyle \displaystyle y=1/x}$ about the x-axis, where x has domain ${\displaystyle \displaystyle [1,\infty )}$. Show whether this surface area exists (integral converges) or diverges. If it exists, provide an upper bound.

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