What's wrong with my sign?

[hank]

Find the volume of the solid whose base is the region bounded by the curves y = sqrt(x) and y = 1/sqrt(x) for [1,4] and whose cross sections perpendicular to the x-axis are squares.

V = S[1-4] sqrt[x]^2 - (1/sqrt(x)^2 dx

I get 3/2 - ln(4).

The book says it should be 3/2 + ln(4).

What am I missing, or is the book wrong?

 

[galactus]

You're sqauring them separately. The region is one side of a square, therefore:

\(\displaystyle \L\\\int_{1}^{4}\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2}dx\)

 

[hank]

Got it, thanks!