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Answer the following questions.
(1) By setting x\plus{}\sqrt{x^2\minus{}1}\equal{}t, find the indefinite integral \int \sqrt{x^2\minus{}1}\ dx.
(2) Given two points

P(p,\ q)\ (p>1,\ q>0)

and

A(1,\ 0)

on the curve x^2\minus{}y^2\equal{}1. Find the area

S

of the figure bounded by two lines

OA,\ OP

and the curve in terms of

p

.
(3) Let S\equal{}\frac{\theta}{2}. Express

p,\ q

in terms of

\theta

530

Problems(1)