The region bounded by y=xe−xy=xe^{-x}y=xe−x, the xxx-axis and the lines x=0x=0x=0 and x=1x=1x=1 is rotated through 2π 2\pi\,2π radians about the xxx-axis.
Find the exact volume of the solid formed.
363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.