09: x In x dx (a) Use integration by parts to nd I . (b) The diagram shows part of the curve with equation 3" = \"Eh\" . J' The shaded region R is bounded by the curve I'VE\" , the line x = e and the x-axis from x = 1 to x = e. Find the volume of the solid generated when the region R is rotated through 360 about the x-axis, giving your answer in an exact form