Calculus Question

Quote:

Originally Posted by frozenflames

84. The base of a solid S is the region enclosed by the graph of y = (lnx)^(1/2), the line x = e, and thex-axis. If the cross sections of S perpendicular to the x-axis are squares, then the volume of S is

(A)12
(B)23
(C) 1
(D) 2
(E)13(e3-1)

The formula is,
$\int^a_bA(x)dx$ . Thus, you need to find a function for the area of each cross section $A(x)$ . Since, the base is $\sqrt{\ln(x)}$ its height is also that because it forms square cross sections. Since, the area of the square is the sides squared we have $A(x)=(\sqrt{\ln x})^2=\ln x$ . Now find the $a,b$ the problem says from the x-axis until x=e. To find the x-axis find when it is zero. Thus, $\sqrt{\ln x}=1$ which happens at $x=0$ . Thus,
$V=\int^e_1\ln xdx=1$