[SOLVED] area infinite, volume finite

The region P is bounded by the x axis , the line x =1 and the curve y = 1/x. show that

a. the area of region P is infinite.

b. show that the solid of revolution obtained by rotating region P about the x axis is finite.

a. $\displaystyle A = \int_{1}^{\infty}\frac{1}{x} dx = \lim_{t \rightarrow \infty} \ln (x) \mid_{1}^{t} = \infty - \ln(1)$ diverges

b. $\displaystyle V = \pi \int_{1}^{\infty} \frac{1}{x^2} dx = \lim_{t \rightarrow \infty} \pi(-\frac{1}{x}) \mid_{1}^{t} = \pi(0 + 1) = \pi$

Am I correct?