1. O is the origin and A is the point on the curve y=tan x where $\displaystyle x=\frac{\pi}{3}.$

Calculate the area of the region R enclosed by the arc OA, the x-axis and the line $\displaystyle x=\frac{\pi}{3}$, giving your answer in EXACT form. Hence, find $\displaystyle \int^{\sqrt3} _0 tan^{-1} y dy$ in EXACT form.

Then, the region S is enclosed by the arc OA, the y-axis ad the line $\displaystyle y=\sqrt3$.

*Find the volume of the solid of revolution formed when S is rotated through *$\displaystyle 2\pi$

* about the x-axis, giving your answer in EXACT form.*

for qn 1 :

i can do the first part....my ans is $\displaystyle \ln2$

i can do the second part too by using integration by parts....my ans is $\displaystyle \frac{\pi \sqrt3}{3}-\ln2$

then I don't know how to do the last part. if it is rotated about y-axis , then i know, but it is rotated about the x-axis.

then ...i'm stuck....