In xyz space, consider two points P(1,\ 0,\ 1),\ Q(\minus{}1,\ 1,\ 0). Let S be the surface generated by rotation the line segment PQ about x axis. Answer the following questions.
(1) Find the volume of the solid bounded by the surface S and two planes x\equal{}1 and x\equal{}\minus{}1.
(2) Find the cross-section of the solid in (1) by the plane y\equal{}0 to sketch the figure on the palne y\equal{}0.
(3) Evaluate the definite integral \int_0^1 \sqrt{t^2\plus{}1}\ dt by substitution t\equal{}\frac{e^s\minus{}e^{\minus{}s}}{2}.
Then use this to find the area of (2). calculusintegrationgeometrygeometric transformationrotationtrigonometrycalculus computations