MathDB

787

Part of 2012 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 787

Source: 2012 Waseda University entrance exam/Science and Technology

2/17/2012
Take two points A (−1, 0), B (1, 0)A\ (-1,\ 0),\ B\ (1,\ 0) on the xyxy-plane. Let FF be the figure by which the whole points PP on the plane satisfies π4≤∠APB≤π\frac{\pi}{4}\leq \angle{APB}\leq \pi and the figure formed by A, BA,\ B.
Answer the following questions:
(1) Illustrate FF.
(2) Find the volume of the solid generated by a rotation of FF around the xx-axis.
calculusintegrationgeometrygeometric transformationrotationlimittrigonometry