Science:Math Exam Resources/Courses/MATH103/April 2005/Question 05 (c)/Statement

Consider the curve given by

$\displaystyle y=f(x)={\frac {1}{x^{p}}}$

for $\displaystyle 1\leq x\leq B$ where $\displaystyle p,B$ are constants with $\displaystyle B>1$ and $\displaystyle p>0$.

Refer to parts (a) and (b) for the values of A (the area between the curve and the x-axis) and V (the volume obtained by rotating the curve about the x-axis).

(c) Now consider the limit as B tends to infinity. For what range of values of the constant p is it true that the volume V has a finite limit while the area A becomes infinite? Explain your answer in terms of your calculations from parts (a) and (b) using one sentence.